Deck 10: Surfaces and Solids

Question 1

A prism and pyramid have congruent bases and the same length of altitude. If the volume of the pyramid is 24 , find the volume of the prism.

Answer 1

NOT ANSWERED.

Question 2

For the regular square pyramid shown, each base edge is 10 cm long. If the pyramid has an altitude of 12 cm, find the length l of the slant height..

A)5 cm
B)12 cm
C)13 cm
D)None of These

Answer 2

C

Question 3

Prisms and pyramids are types of polyhedrons.

Answer 3

False

Question 4

For the right triangular prism shown, the sides of the base measure 6 cm, 8 cm, and 10 cm. If the height of the prism is 12 cm, find the total area of the prism.

Question 5

For a right rectangular prism with dimensions l, w, and h, the volume V is given by V = lwh.

Question 6

The lateral area L of any prism whose altitude measures h and whose base has perimeter P is given by L = hP.

Question 7

A right pyramid has a rectangular base that is 6 ft by 8 ft. If the altitude of the pyramid is 10 feet, find its volume.

A)80
B)160
C)240
D)480

Question 8

A right prism has height h and perimeter P for its base. Write the formula for the lateral area L of the prism.

Question 9

For the triangular prism, the areas of the lateral faces are 18 , 26 , and 34 . If the area of the base is 16 , find the total area of the prism.

Question 10

For the right rectangular prism (or box)shown, the dimensions are l = 12 in, w = 4 in,and h = 3 in. How long is a diagonal of the box?

Question 11

A right rectangular prism has a base that measures 6 in by 8 in. If the volume of the "box" is 360 , find the height of the prism.

Question 12

What is the total number of faces for a prism whose base is a decagon?

Question 13

Let n represent the number of vertices in the base of a prism. In terms of n, how many edges does the prism have?

Question 14

Find the lateral area for a regular hexagonal prism in which the base edges are 4 inches long and the altitude is h = 6 inches.

A)36
B)72
C)144
D)None of These

Question 15

Where B is the area of the base and h is the length of altitude, the volume of a prism and cylinder can both be found by the formula V = Bh.

Question 16

In a prism, the two bases are parallel to each other and congruent to each other.

Question 17

One pyramid has a volume of 356 . A larger pyramid has base edges twice as long as that of the first pyramid and a height that is 3 times the height of the first pyramid. What is the volume of the larger pyramid?

Question 18

If a lateral edge is perpendicular to a base edge, then the prism shown is a regular triangular prism.

Question 19

An octagonal prism has 9 faces.

Question 20

For the right triangular prism shown, the base is a right triangle with sides of lengths 3 in, 4 in, and 5 in. If the prism has a height of 6 inches, find its volume.

A)24
B)36
C)72
D)360

Question 21

For a triangle with sides of lengths 13 cm, 14 cm, and 15 cm, the altitude to the 14 cm side separates that side into segments of lengths 5 cm and 9 cm. For the solid of revolution determined by revolving the triangular region about the 14 cm side, find its volume.

Question 22

For a right circular cylinder with radius of base r and length of altitude h, the formula for the lateral area L is:

A)
B)
C)
D)None of These

Question 23

For a regular square pyramid, each side of the base is 6 inches long. If the altitude of the pyramid measures 9 inches, find the length of each lateral edge correct to the nearest tenth of an inch.

Question 24

For a regular pentagonal pyramid, each lateral face has an area of 12 . If the area of the pentagonal base is 15 , find the total (surface)area of the pyramid.

A)75
B)90
C)87
D)102

Question 25

If the base of the pyramid shown is a square, then the pyramid is a regular square pyramid.

Question 26

Each lateral face of a regular hexagonal pyramid has lateral edges of length 10 inches and a base edge of 12 inches. What is the lateral area of the pyramid?

A)48
B)288
C)384
D)

Question 27

A regular square pyramid has base edges of 9 inches and an altitude length of 12 inches. Find the volume of the pyramid.

Question 28

With O as the center of the regular pentagonal base and P as the vertex of the pyramid shown, what relationship must hold in order for the pyramid to be known as a regular pentagonal pyramid?

Question 29

The formula for the volume of a right circular cylinder of radius r and altitude h is given by .

Question 30

Like the pyramid, the volume formula for a right circular cone can be expressed as . State another form of the formula for the volume of the cone.

Question 31

A right circular cone has a radius of 6 inches and an altitude of 8 inches. Use in order to find the exact total area of the cone.

Question 32

For the pyramid with base area B and altitude length h , the volume is .

Question 33

Each base edge of a regular pentagonal pyramid measures 10 cm. If the lateral area of this pyramid is 425 , find the length of the slant height of the pyramid.

Question 34

A pyramid has a square base with sides of length e. If the altitude of the pyramid also measures e, what is the volume of the pyramid?

Question 35

A church steeple that needs to be reshingled has the shape of a regular square pyramid. If base edges of the steeple measure 16 feet while lateral edges measure 17 feet, what is the lateral area (area to reshingle)of the steeple?

Question 36

Given a regular square pyramid, with respect to which figure(s)does this pyramid have symmetry . . . a point, a line, or a plane?

Question 37

For a pentagonal pyramid, the total number of edges is 10.

Question 38

A right circular cylinder and a right circular cone with the same circular base and same length of altitude will have the same volume.

Question 39

With a base of n sides of length s , the lateral area L of a regular pyramid can be written . Using P for perimeter, write the more common form of this formula

Question 40

In the form , verify Euler's Formula for the pyramid shown.

Question 41

A storage tank is in the shape of a right circular cylinder. If r = 3 ft and h = 4 ft,find the exact volume of the cylinder.

Question 42

Correct to the nearest tenth of a square foot, find the surface area of a sphere that has a diameter of length 12.8 feet. Use the calculator value of .

A)257.4
B)514.7
C)549.0
D)1098.1

Question 43

The total area for a regular octahedron is . Find the length of each edge of the octahedron.

A)4 cm
B)8 cm
C)12 cm
D)None of These

Question 44

A food container is in the shape of a right circular cylinder. To the nearest cubic inch, find the exact volume of the food container if the radius of the base measures 2.3 inches and the height of the container is 6.2 inches.

A)52
B)76
C)92
D)103

Question 45

Using , find the approximate volume of the sphere with radius 7 inches. Provide result correct to nearest tenth of cubic inch.

Question 46

The volume of a right circular cone is exactly . If the altitude of the cone has a length of 12 feet, what is the length of radius of the circular base?

A)4 ft
B)4.25 ft
C)4.5 ft
D)4.75 ft

Question 47

Find the volume of the box that has dimensions of 10 cm, 12 cm, and 16 cm.

Question 48

Given that 1 foot = 12 inches, how many cubic inches are in one cubic foot?

Question 49

For a right circular cone, the altitude has the same measure as its radius. If the volume of the cone is approximately 56 , find the length of radius to the nearest tenth of a foot.

Question 50

For the regular dodecahedron with faces numbered 1, 2, 3, . . . , 12, what is the probability that one roll produces a result for 6 or larger? Provide the answer as a common fraction.

Question 51

A right circular cylinder of altitude h and with a base of radius r has lateral area L where .

Question 52

A right circular cone has a diameter for its base of length 16 inches and an altitude of 15 inches. Use to find the exact lateral area of the cone.

A)
B)
C)
D)None of These

Question 53

Find the length of slant height l of a right circular cone for which the length of radius is r = 3 cm and the altitude measures h = 4 cm.

Question 54

Given that m = 90 ° and that the triangular region is revolved about side , the related solid of revolution is a right circular cone with radius BC and altitude AC .

Question 55

Use to find the exact total area of the right circular cone for which r = 3 cm and l = 5 cm.

Question 56

For a right circular cylinder, the length of radius of base is 2.3 inches and the altitude measures 8.5 inches. Correct to the nearest tenth of cubic inch, find the volume of the cylinder.

Question 57

Where m = 90 ° , the solid of revolution determined by revolving right triangle about leg is a right circular cone.

Question 58

The volume of a cube is 8 . Find the volume of a cube whose edges are twice those of the first cube.

A)16
B)32
C)48
D)64

Question 59

A regular dodecahedron is manufactured as a desk calendar. What is the likelihood that the month facing upward is a month that begins with the letter "J?"

A)
B)
C)
D)

Question 60

The total area of a right circular cylinder is . If the height of the cylinder is 4,find the length of the radius.

Question 61

How many edges does a regular octahedron have?

A)12
B)10
C)8
D)16

Question 62

For a box, its height is 4 feet and its volume is 192 . If the length of the rectangular base is 2 feet more than the width of the base, find the width of the base.

A)6 ft
B)8 ft
C)12 ft
D)16 ft

Question 63

A cube has the volume of 45.6 . Which expression represents the length of each edge of the cube?

A) in
B) in
C)15.2 in
D)None of These

Question 64

A regular icosahedron has its faces numbered 1, 2, 3, . . . , 20 and is used as a die. What is the probability that a roll produces a multiple of 5?

Question 65

Given that 1 yard = 3 feet, find the number of cubic feet in 1 cubic yard.

A)27
B)9
C)3
D)None of These

Question 66

What is the exact surface area for a ball with radius 5 inches?

Question 67

The 8 faces of a regular octahedron are congruent equilateral triangles.

Question 68

For a given polyhedron, there are 24 vertices and 32 faces. How many edges does the polyhedron have? [Hint: .]

Question 69

A sphere is circumscribed about a cube that has edges of 4 cm. Correct to nearest tenth of a square centimeter, find the approximate surface area for the sphere. Use the calculator value of .

Question 70

For the right circular cylinder, the base has area and the lateral area is . What is the total area of the cylinder?

Question 71

The volume V of a sphere with a diameter of length d can be written .

Question 72

Given that each edge measures 4 cm, find the total area of the regular tetrahedron.

A)
B)
C)
D)

Question 73

The volume of a cube whose sides each measure 1 yard can be written as 9 .

Question 74

The volume of a sphere is 564 . Correct to the nearest tenth of a meter, find the length of the radius of the sphere.

A)6.2 m
B)5.7 m
C)5.4 m
D)5.1 m

Question 75

In a polyhedron, the relationship between numbers of vertices V , edges E , and faces F is found in Euler's equation .

Question 76

If the edges of a cube are doubled, then the volume of the new cube will be exactly twice the volume of the original cube.

Question 77

What is the name of the geometric figure that is the theoretical limit of an "inscribed" regular polyhedron whose number of faces increases without limit?

Question 78

The surface area of a regular hexahedron is 102 . To the nearest tenth of a centimeter, what is the length of each edge of the hexahedron?

Question 79

What is the exact volume for the solid that results when the semicircular region shown is rotated about its diameter of length 6 inches?