Deck 9: Geometry

Question 1

If the surface area of a cylinder excluding the top and bottom is equal to the volume of the cylinder, what is the radius of the cylinder?

A)1
B)2
C)
D)3

Answer 1

B

Question 2

A right triangle has legs of length 3 and 4. If the hypotenuse is the diameter of a circle, what is the area of the circle?

A)
B)
C)
D)

Answer 2

B

Question 3

Town B is 6 miles due north of town A, and town C is due east of town A. It is 11 miles from town B to town C. Find the distance from town A to town C.

A)5 miles
B)5.8 miles
C)8.6 miles
D)9.2 miles

Answer 3

D

Question 4

If a circle has the circumference of length 3.14, what is the diameter of the circle?

A)
B)
C)
D)

Question 5

A soup can has a diameter of 2.75 inches and a height of 4.25 inches. How many square inches of metal are required to make the soup can?

A)
B)
C)
D)

Question 6

A soup can has a diameter of 2.75 inches and a height of 4.25 inches. When you open the soup can, how far does the can opener travel?

A)4.32 inches
B)5.97 inches
C)7.00 inches
D)8.64 inches

Question 7

Heron's formula gives the area of a triangle if we know the perimeter of the triangle.

Question 8

The _______________ of a geometric figure is the distance around it.

A)area
B)volume
C)perimeter
D)height

Question 9

A circular swimming pool is 20 feet across and is enclosed by a fence. How long is the fence?

A)20.0 feet
B)31.4 feet
C)62.8 feet
D)71.4 feet

Question 10

A soup can has a diameter of 2.75 inches and a height of 4.25 inches. Find the volume of the soup can.

A)
B)
C)
D)

Question 11

Find the length of the hypotenuse of a right triangle whose legs have lengths 4 and 9.

A)9.8
B)10.7
C)11.2
D)13.5

Question 12

The length of the hypotenuse of a right triangle is 10 and a leg has length 3. Find the length of the other leg.

A)8.7
B)7.9
C)9.5
D)8.2

Question 13

If a circle has a circumference of 10, what is the area of the circle?

A)
B)
C)
D)

Question 14

A restaurant serves soda in cylindrical pitchers that are 6 inches in diameter and 10 inches tall. What is the volume of the pitcher?

A)
B)
C)
D)

Question 15

A triangle with sides of length 8, 15, and 17 is a right triangle.

Question 16

If a cylinder has radius r and height h, then its volume is given by:

A)
B)
C)
D)

Question 17

A restaurant serves soda in cylindrical pitchers that are 6 inches in diameter and 10 inches tall. If the pitcher has a 1-inch head of foam, how much soda is lost as a result?

A)
B)
C)
D)

Question 18

Find the area of a right triangle whose legs have lengths 3 and 4.

A)18
B)14
C)12
D)6

Question 19

The hypotenuse of a right triangle has length 13, and a leg has length 5. Find the area of that triangle.

A)30
B)32.5
C)60
D)65

Question 20

A soup can has a diameter of 2.75 inches and a height of 4.25 inches. How many square inches of paper are required to cover the surface of the can excluding the top and bottom?

A)
B)
C)
D)

Question 21

Two triangles are _______________ if all corresponding angles have the same measure.

A)equal
B)similar
C)equivalent
D)scalene

Question 22

If a variable quantity A is proportional to another quantity B with proportionality constant c, then B is proportional to A with proportionality constant:

A)
B)
C)
D)

Question 23

The area of a pizza is proportional to the ___________ of the radius.

A)reciprocal
B)square root
C)square
D)cube

Question 24

One variable quantity is (directly) proportional to another if it is always a fixed (nonzero) constant multiple of the other.

Question 25

I have a triangular yard whose lengths measure 50, 60, and 70 feet. I want to fertilize my lawn with bags of fertilizer that cover 400 square feet each. How many bags of fertilizer will I need to buy?

A)2
B)3
C)4
D)5

Question 26

Consider a box with a square base and a height of 6 inches. Then the volume of the box is proportional to the area of the base. What is the constant of proportionality?

A)3
B)6
C)12
D)36

Question 27

Quantity A is proportional to quantity B if there is a nonzero constant c such that:

A)
B)
C)
D)

Question 28

The surface area of a ball with radius is given by . If a soccer ball has a diameter of 8.65 inches, what is its surface area?

A)
B)
C)
D)

Question 29

A(n) _______________ is a rectangle for which that ratio of the length to the width is the golden ratio $\phi$ .

A)silver rectangle
B)Euclidian rectangle
C)golden rectangle
D)Pythagorean rectangle

Question 30

The volume of a ball with radius is given by . If a soccer ball has a diameter of 8.65 inches, what is its volume?

A)
B)
C)
D)

Question 31

For similar triangles, the lengths of corresponding sides are:

A)equal.
B)doubled.
C)equivalent.
D)proportional.

Question 32

I have a triangular yard whose lengths measure 50, 60, and 70 feet. What is the area of my yard?

A)
B)
C)
D)

Question 33

The shorter side of a golden rectangle is 6 inches. How long is the longer side?

A)7.6 inches
B)9.7 inches
C)9.2 inches
D)8.8 inches

Question 34

If each step of a staircase rises 9 inches, then the height of the staircase above the base is proportional to the number of steps. What is the constant of proportionality?

A)9
B)6
C)4.5
D)3

Question 35

The radius of a circle is proportional to the square root of the area. What is the constant of proportionality?

A)
B)
C)
D)

Question 36

An isosceles triangle has a base of 20 units and a height of 24 units. Find the perimeter of the triangle.

A)64 units
B)68 units
C)72 units
D)80 units

Question 37

If two of the three pairs of corresponding angles of a triangle have the same measure, then the triangles are:

A)similar.
B)congruent.
C)equivalent.
D)identical.

Question 38

What is the golden ratio $\phi$ ?

A)
B)
C)
D)

Question 39

The size of a monitor (also called a display) is usually measured in terms of the diagonal size of the rectangle. If a monitor measures 13.2 inches by 17.8 inches, what is the length of the diagonal?

A)31.0 inches
B)22.2 inches
C)15.5 inches
D)18.7 inches

Question 40

You need to order cement to make a concrete sidewalk 3 feet wide and 75 feet long. Assume that the depth of the concrete is 4 inches. How much cement is needed, in cubic feet?

A)
B)
C)
D)

Question 41

The volume of a sphere with radius is given by Suppose a child is offered a balloon but wants one that has twice the radius of the one offered. How does the increase in radius affect the amount of gas in the balloon?

A)It will be 2 times as much.
B)It will be 4 times as much.
C)It will be 8 times as much.
D)It will be 16 times as much.

Question 42

Suppose a box has a fixed height of 4 feet and a square base. The length of one of the sides of the base is proportional to the square root of the volume. What is the constant of proportionality?

A)4
B)
C)2
D)

Question 43

A planar figure has _______________ symmetry about a point if it remains exactly the same after a rotation about that point of less than 360 degrees.

A)reflectional
B)rotational
C)tiling
D)proportional

Question 44

Which rotational symmetry does a square have?

A)30 degrees
B)45 degrees
C)60 degrees
D)90 degrees

Question 45

The volume of a cylinder with radius r and height h is given by . If the height of a cylindrical can is held constant, the volume is proportional to the radius squared. What is the constant of proportionality?

A)
B)
C)
D)

Question 46

The perimeter of a square is proportional to the square root of the area. What is the constant of proportionality?

A)2
B)4
C)8
D)16

Question 47

Suppose a cone has height h and the radius of its top circle is r. Then the volume is given by . Two ice cream cones have the same height but one cone's radius is three times the radius of the other. Compare the amount of ice cream the cones can hold.

Question 48

A _______________ tiling is a tiling of the plane that consists of repeated copies of a single regular polygon, meeting edge to edge.

A)similar
B)proportional
C)golden
D)regular

Question 49

The surface area of a sphere with radius r is given by . The amount of paint needed to color a billiard ball of radius r is proportional to:

A)
B)
C)
D)

Question 50

The volume of a sphere with radius is given by . The amount of gas in a balloon of radius r is proportional to

A)
B)
C)
D)

Question 51

The surface area of a cone with height and radius (of its top) is given by . If the radius of the top is held constant, the surface area is proportional to:

A)
B)
C)
D)None of the above.

Question 52

The triangles below are similar. Find the length of side x.

A)6.2
B)7.1
C)5.8
D)6.7

Question 53

The basal metabolic rate (BMR) of an animal is a measure of the amount of energy it needs for survival. An animal with a larger BMR will need more food to survive. One simple model for the BMR states that among animals of a similar shape, the rate is proportional to the square of the length. If one animal is 5 times as long as another, how much larger is its BMR compared to the smaller animal?

A)
B)5 times
C)10 times
D)25 times

Question 54

A pole casts a 5-foot shadow, and at the same time a 6-foot tall man casts a 2-foot shadow. How tall is the pole?

A)20 feet
B)18 feet
C)15 feet
D)12 feet

Question 55

The longer side of a golden rectangle is 12 inches. How long is the shorter side?

A)7.4 inches
B)10.4 inches
C)19.4 inches
D)9.4 inches

Question 56

In a regular tiling, if there are six polygons meeting at a vertex, then the angles at the vertex are _______ degrees.

A)45
B)60
C)90
D)120

Question 57

The area of an equilateral triangle is proportional to the square of a side. If all of the sides of an equilateral triangle are doubled, what happens to the area?

A)It stays the same.
B)It is doubled.
C)It is tripled.
D)It is quadrupled.

Question 58

A planar figure has _______________ symmetry about a line L if the figure is identical to its reflection through L.

A)reflectional
B)rotational
C)tiling
D)proportional

Question 59

Suppose a box has a fixed height of 4 feet and a square base. The length of one of the sides of the base is proportional to the square root of the volume. What is the constant of proportionality?

A)14 feet
B)16 feet
C)18 feet
D)20 feet

Question 60

The triangles below are similar. Find the length of side y.

A)2.3
B)2.9
C)3.7
D)4.5

Question 61

Which rotational symmetry does a rectangle have?

A)45 degrees
B)90 degrees
C)180 degrees
D)270 degrees

Question 62

If a planar figure has reflectional symmetry about a line, then the figure also has a rotational symmetry.

Question 63

If denotes a clockwise rotation of the plane through an angle of degrees, we use to mean that we make a clockwise rotation of the plane through an angle of degrees n times. Find between 0 and 360 degrees so that .

A)270 degrees
B)180 degrees
C)220 degrees
D)150 degrees

Question 64

Which of the following regular figures have a 45-degree rotational symmetry?

A)pentagon
B)hexagon
C)octagon
D)dodecagon

Question 65

Which regular polygon cannot be regularly tiled in the plane?

A)square
B)triangle
C)hexagon
D)octagon

Question 66

If denotes a clockwise rotation of the plane through an angle of degrees, we use to mean that we make a clockwise rotation of the plane through an angle of degrees n times. Find n so that .

A)6
B)8
C)10
D)11

Question 67

If denotes a clockwise rotation of the plane through an angle of degrees, we use to mean that we make a clockwise rotation of the plane through an angle of degrees n times. What is the result of ?

A)A rotation through 45 degrees
B)A rotation through 90 degrees
C)A rotation through 180 degrees
D)A rotation through 360 degrees

Question 68

Find the rotational symmetries of a regular eight-pointed star.

A)30 degrees and multiples
B)45 degrees and multiples
C)60 degrees and multiples
D)90 degrees and multiples

Question 69

How many reflectional symmetries does a square have?

A)4
B)3
C)2
D)1

Question 70

If denotes a clockwise rotation of the plane through an angle of degrees, we use to mean that we make a clockwise rotation of the plane through an angle of degrees n times. Find between 0 and 360 degrees so that .

A)
B)
C)
D)