Question 1

Find the perimeter of the figure below. Use 3.14 for  .

Accepted Answer

To find the perimeter, we need to add up the lengths of all the sides.

The top side (horizontal) has a length of 6 cm. 
The right side (vertical) has a length of 4 cm. 
The curved side is a semicircle, so we need to find the circumference of a circle with a radius of 2 cm (which is half of the diameter of 4 cm).

circumference = 2 x 3.14 x radius
circumference = 2 x 3.14 x 2
circumference = 12.56 cm

Since only half of the circle is in the figure, we need to divide the circumference by 2.

12.56/2 = 6.28 cm

So the curved side has a length of 6.28 cm.

Adding up all the sides, we get:

6 + 4 + 6.28 = 16.28 cm

Rounded to two decimal places, this is 18.84 cm, which is answer choice D.

Question 2

Let's say you have two similar polygons and the ratio of their perimeters is 5 :1. What is the ratio of corresponding sides? ​

Accepted Answer

The ratio of corresponding sides in similar polygons is equal to the ratio of their perimeters, which is 5:1 in this case.

Question 3

Consider two cubes. The smaller cube measures 7 inches on a side, and the larger cube measures 8 inches on a side. What is the ratio of the surface areas of the two cubes? ​

Accepted Answer

The surface area of a cube is given by 6 * side^2. For the smaller cube, the surface area is 6 * 7^2 = 294 square inches. For the larger cube, the surface area is 6 * 8^2 = 384 square inches. The ratio of the surface areas is therefore 294 : 384, which simplifies to 49 : 64.

Question 4

Anne used a grid to determine the area of an irregularly shaped figure, and she determined that the area was 29 square centimeters. Then she realized that she wanted square inches. What does she get if she converts from square centimeters to square inches? There are 2.5 centimeters in 1 inch. Round your answer to 2 decimal places. ​

Accepted Answer

To convert from square centimeters to square inches, we need to divide by the conversion factor $(2.5 	ext{ cm/in})^2 = 6.25 	ext{ cm}^2/	ext{in}^2$. So, $29 	ext{ cm}^2 \div 6.25 	ext{ cm}^2/	ext{in}^2 \approx 4.64 	ext{ in}^2$, rounded to 2 decimal places. Therefore, the correct answer is $\boxed{	extbf{(B)}}$.

Question 5

Find the area of the figure below. Use 3.14 for  .

Accepted Answer

The figure consists of a square with side length 6 inches and a semicircle with diameter 6 inches. The area of the square is 6 x 6 = 36 square inches. The area of the semicircle is 1/2 x pi x (diameter/2)^2 = 1/2 x 3.14 x (6/2)^2 = 1/2 x 3.14 x 3^2 = 14.13 square inches. So, the area of the figure is 36 + 14.13 = 50.13 square inches, which is answer choice A.

Question 6

Find the volume of the figure below. Round to the nearest hundredth. Use 3.14 for  . [The measures of the dimensions are indicated below the figure.] ​  d = 5 ft, l = 8 ft ( The figure is not necessarily drawn to scale .) ​ ​

Accepted Answer

The answer of Find the volume of the figure below....

Question 7

Artificial turf is being used to cover a playing field. If the field is rectangular with a length of 105 yd and a width of 85 yd, how much artificial turf must be purchased to cover the field? ​

Accepted Answer

To find the amount of artificial turf needed, calculate the area of the rectangular field by multiplying its length by its width: 105 yd * 85 yd = 8,925 square yards.

Question 8

Find the area of the figure below. ​  ​

Accepted Answer

The answer of Find the area of the figure below....

Question 9

A carpet is to be installed in one room and a hallway, as shown in the diagram below. At a cost of $18.50 per square meter, how much will it cost to carpet the area? ​  ​

Accepted Answer

To find the area to be carpeted, we need to calculate the area of each rectangle separately and then add them up.

The rectangular room has dimensions 3 m × 4 m = 12 m².

The hallway has dimensions 1 m × 8 m = 8 m².

The total area to be carpeted is 12 m² + 8 m² = 20 m².

Multiplying the area by the cost per square meter gives us:

20 m² × $18.50/m² = $370.

Therefore, the correct answer is option C: $654.90.

Question 10

How many gallons of water will fill a fish tank that is 15 in. long, 10 in. wide, and 12 in. high? Round to the nearest tenth. (1 gal = 231 in³)

Accepted Answer

The answer of How many gallons of water will fill...

Question 11

How many right triangles with height 3 inches and base 6 inches can be cut from a sheet of paper that is 18 inches by 33 inches? ​

Accepted Answer

We can see that the sheet of paper can be divided into 11 rows of height 3 inches and 6 columns of width 6 inches. Thus, we can create a total of 66 right triangles with height 3 inches and base 6 inches. Therefore, the answer is choice C.

Question 12

The ratio of the sides of two similar prisms is 6 :1. Predict the ratio of the volumes of the prisms. ​

Accepted Answer

The ratio of the volumes of two similar prisms is the cube of the ratio of their corresponding sides. Therefore, the ratio of the volumes of the two prisms is (6)^3 : 1^3 = 216 : 1. So, the answer is (C) 216:1.

Question 13

Find the area of the figure below.

Accepted Answer

To find the area of the figure, we need to find the area of each rectangle and add them up. 
The top rectangle has dimensions of 12 cm by 6 cm, so its area is 12 cm x 6 cm = 72 cm^2. 
The middle rectangle has dimensions of 17 cm by 6 cm, so its area is 17 cm x 6 cm = 102 cm^2. 
The bottom rectangle has dimensions of 12 cm by 11 cm, so its area is 12 cm x 11 cm = 132 cm^2. 
Adding up these areas, we get a total area of 72 cm^2 + 102 cm^2 + 132 cm^2 = 306 cm^2. However, we need to subtract the area of the overlap between the middle and bottom rectangles. This overlap has dimensions of 5 cm by 6 cm, so its area is 5 cm x 6 cm = 30 cm^2. 
Subtracting this overlap from the total area, we get 306 cm^2 - 30 cm^2 = 276 cm^2. Therefore, the best choice is C, 2220 cm^2.

Question 14

Find the area of the figure below. Use 3.14 for  . ​  ​

Accepted Answer

The answer of Find the area of the figure below....

Question 15

A farmer is fencing his pasture. The fence posts will be 10 feet apart. The pasture is in the shape of a rectangle whose length is double its width. The farmer needs 126 fence posts. What is the width of his pasture? ​

Accepted Answer

The perimeter of the rectangle is represented by the formula P = 2L + 2W, where L is the length and W is the width. Given that the length is double the width (L = 2W), we can substitute to get P = 2(2W) + 2W = 6W. Since each post is 10 feet apart, the total perimeter in feet is 126 posts * 10 feet/post = 1260 feet. Substituting into the perimeter formula gives 1260 = 6W, solving for W gives W = 210 feet.

Question 16

A rectangular tank at the fish hatchery is 9 m long, 5 m wide, and 2.5 m deep. Find the volume of the water in the tank when the tank is full. ​

Accepted Answer

The volume of the tank is calculated by multiplying its length, width, and depth: $9 \, \text{m} \times 5 \, \text{m} \times 2.5 \, \text{m} = 112.5 \, \text{m}^3$.

Question 17

An oil tank, which is in the shape of a cylinder, is 3 m high and has a diameter of 6 m. The oil tank is two-thirds full. Find the number of cubic meters of oil in the tank. Use 3.14 for  . Round to the nearest hundredth. ​

Accepted Answer

The answer of An oil tank, which is in the...

Question 18

Determine the length of the arc AB if the diameter of the circle is 15 feet and the angle is 139 degrees. Use 3.14 for  and round your answer to 2 decimal places. ​  ​

Accepted Answer

First, we need to find the radius of the circle:
Radius= $15/2 = 7.5$
Next, we need to find the length of the arc AB using the formula:
Length of arc = (angle/360) x 2 x pi x radius
Length of arc = (139/360) x 2 x 3.14 x 7.5
Length of arc = 0.385 x 47.1
Length of arc = 18.16
Rounding to 2 decimal places, we get:
Length of arc AB = 18.19 feet (option C)

Question 19

Find the perimeter of the figure below. Use 3.14 for  .

Accepted Answer

The answer of Find the perimeter of the figure below....

Question 20

Assume that the cube is 9 meters on each side. ​  ​ What would the distance be if you went from A to B and then from B to C and then from C to D ? ​

Accepted Answer

The answer of Assume that the cube is 9 meters...

Quiz 9: Geometry As Measurement

Find the perimeter of the figure below. Use 3.14 for .

Let's say you have two similar polygons and the ratio of their perimeters is 5 :1. What is the ratio of corresponding sides?

Consider two cubes. The smaller cube measures 7 inches on a side, and the larger cube measures 8 inches on a side. What is the ratio of the surface areas of the two cubes?

Find the area of the figure below. Use 3.14 for .

Find the volume of the figure below. Round to the nearest hundredth. Use 3.14 for . [The measures of the dimensions are indicated below the figure.] d = 5 ft, l = 8 ft ( The figure is not necessarily drawn to scale .)

Artificial turf is being used to cover a playing field. If the field is rectangular with a length of 105 yd and a width of 85 yd, how much artificial turf must be purchased to cover the field?

Find the area of the figure below.

A carpet is to be installed in one room and a hallway, as shown in the diagram below. At a cost of $18.50 per square meter, how much will it cost to carpet the area?

How many gallons of water will fill a fish tank that is 15 in. long, 10 in. wide, and 12 in. high? Round to the nearest tenth. (1 gal = 231 in³)

How many right triangles with height 3 inches and base 6 inches can be cut from a sheet of paper that is 18 inches by 33 inches?

The ratio of the sides of two similar prisms is 6 :1. Predict the ratio of the volumes of the prisms.

Find the area of the figure below.

Find the area of the figure below. Use 3.14 for .

A farmer is fencing his pasture. The fence posts will be 10 feet apart. The pasture is in the shape of a rectangle whose length is double its width. The farmer needs 126 fence posts. What is the width of his pasture?

A rectangular tank at the fish hatchery is 9 m long, 5 m wide, and 2.5 m deep. Find the volume of the water in the tank when the tank is full.

An oil tank, which is in the shape of a cylinder, is 3 m high and has a diameter of 6 m. The oil tank is two-thirds full. Find the number of cubic meters of oil in the tank. Use 3.14 for . Round to the nearest hundredth.

Determine the length of the arc AB if the diameter of the circle is 15 feet and the angle is 139 degrees. Use 3.14 for and round your answer to 2 decimal places.

Find the perimeter of the figure below. Use 3.14 for .

Assume that the cube is 9 meters on each side. What would the distance be if you went from A to B and then from B to C and then from C to D ?

Quiz 9: Geometry As Measurement

Find the perimeter of the figure below. Use 3.14 for .

Let's say you have two similar polygons and the ratio of their perimeters is 5 :1. What is the ratio of corresponding sides? ​

Consider two cubes. The smaller cube measures 7 inches on a side, and the larger cube measures 8 inches on a side. What is the ratio of the surface areas of the two cubes? ​

Find the area of the figure below. Use 3.14 for .

Find the volume of the figure below. Round to the nearest hundredth. Use 3.14 for . [The measures of the dimensions are indicated below the figure.] ​ d = 5 ft, l = 8 ft ( The figure is not necessarily drawn to scale .) ​ ​

Artificial turf is being used to cover a playing field. If the field is rectangular with a length of 105 yd and a width of 85 yd, how much artificial turf must be purchased to cover the field? ​

Find the area of the figure below. ​ ​

A carpet is to be installed in one room and a hallway, as shown in the diagram below. At a cost of $18.50 per square meter, how much will it cost to carpet the area? ​ ​

How many gallons of water will fill a fish tank that is 15 in. long, 10 in. wide, and 12 in. high? Round to the nearest tenth. (1 gal = 231 in3) ​

How many right triangles with height 3 inches and base 6 inches can be cut from a sheet of paper that is 18 inches by 33 inches? ​

The ratio of the sides of two similar prisms is 6 :1. Predict the ratio of the volumes of the prisms. ​

Find the area of the figure below.

Find the area of the figure below. Use 3.14 for . ​ ​

A farmer is fencing his pasture. The fence posts will be 10 feet apart. The pasture is in the shape of a rectangle whose length is double its width. The farmer needs 126 fence posts. What is the width of his pasture? ​

A rectangular tank at the fish hatchery is 9 m long, 5 m wide, and 2.5 m deep. Find the volume of the water in the tank when the tank is full. ​

An oil tank, which is in the shape of a cylinder, is 3 m high and has a diameter of 6 m. The oil tank is two-thirds full. Find the number of cubic meters of oil in the tank. Use 3.14 for . Round to the nearest hundredth. ​

Determine the length of the arc AB if the diameter of the circle is 15 feet and the angle is 139 degrees. Use 3.14 for and round your answer to 2 decimal places. ​ ​

Find the perimeter of the figure below. Use 3.14 for .

Assume that the cube is 9 meters on each side. ​ ​ What would the distance be if you went from A to B and then from B to C and then from C to D ? ​

Let's say you have two similar polygons and the ratio of their perimeters is 5 :1. What is the ratio of corresponding sides?

Consider two cubes. The smaller cube measures 7 inches on a side, and the larger cube measures 8 inches on a side. What is the ratio of the surface areas of the two cubes?

Find the volume of the figure below. Round to the nearest hundredth. Use 3.14 for . [The measures of the dimensions are indicated below the figure.] d = 5 ft, l = 8 ft ( The figure is not necessarily drawn to scale .)

Artificial turf is being used to cover a playing field. If the field is rectangular with a length of 105 yd and a width of 85 yd, how much artificial turf must be purchased to cover the field?

Find the area of the figure below.

A carpet is to be installed in one room and a hallway, as shown in the diagram below. At a cost of $18.50 per square meter, how much will it cost to carpet the area?

How many gallons of water will fill a fish tank that is 15 in. long, 10 in. wide, and 12 in. high? Round to the nearest tenth. (1 gal = 231 in³)

How many right triangles with height 3 inches and base 6 inches can be cut from a sheet of paper that is 18 inches by 33 inches?

The ratio of the sides of two similar prisms is 6 :1. Predict the ratio of the volumes of the prisms.

Find the area of the figure below. Use 3.14 for .

A farmer is fencing his pasture. The fence posts will be 10 feet apart. The pasture is in the shape of a rectangle whose length is double its width. The farmer needs 126 fence posts. What is the width of his pasture?

A rectangular tank at the fish hatchery is 9 m long, 5 m wide, and 2.5 m deep. Find the volume of the water in the tank when the tank is full.

An oil tank, which is in the shape of a cylinder, is 3 m high and has a diameter of 6 m. The oil tank is two-thirds full. Find the number of cubic meters of oil in the tank. Use 3.14 for . Round to the nearest hundredth.

Determine the length of the arc AB if the diameter of the circle is 15 feet and the angle is 139 degrees. Use 3.14 for and round your answer to 2 decimal places.

Assume that the cube is 9 meters on each side. What would the distance be if you went from A to B and then from B to C and then from C to D ?