Question 1

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.

Accepted Answer

The answer of For a triangle with sides of lengths...

Question 2

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

Accepted Answer

The answer of For a right circular cylinder with radius...

Question 3

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.

Accepted Answer

The answer of For a regular square pyramid, each side...

Question 4

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

Accepted Answer

The answer of For a regular pentagonal pyramid, each lateral...

Question 5

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

Accepted Answer

A regular pyramid has a regular polygon as its base and all of its lateral faces are congruent isosceles triangles. Since a square is a regular polygon, if the base of the pyramid is a square, then the pyramid is a regular square pyramid.

Question 6

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)

Accepted Answer

The answer of Each lateral face of a regular hexagonal...

Question 7

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

Accepted Answer

The answer of A regular square pyramid has base edges...

Question 8

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?

Accepted Answer

The answer of With O as the center of the...

Question 9

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

Accepted Answer

The answer of The formula for the volume of a...

Question 10

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.

Accepted Answer

The answer of Like the pyramid, the volume formula for...

Question 11

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.

Accepted Answer

The answer of A right circular cone has a radius...

Question 12

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

Accepted Answer

The formula for the volume of a pyramid is V = (1/3)Bh, where B is the base area and h is the altitude length. Therefore, it is true that the volume of a pyramid with base area B and altitude length h is 1/3*B*h.

Question 13

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.

Accepted Answer

The answer of Each base edge of a regular pentagonal...

Question 14

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?

Accepted Answer

The answer of A pyramid has a square base with...

Question 15

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?

Accepted Answer

The answer of A church steeple that needs to be...

Question 16

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

Accepted Answer

The answer of Given a regular square pyramid, with respect...

Question 17

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

Accepted Answer

A pentagonal pyramid has 5 edges at the base and 5 edges connecting the base vertices to the apex, totaling 10 edges.

Question 18

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

Accepted Answer

The volume of a cylinder is Vc = πr^2h and the volume of a cone is Vco = (1/3)πr^2h, where r is the radius and h is the altitude. Since both the cylinder and cone have the same circular base and length of altitude, they have the same value of r and h. Therefore, their volumes are equal, as Vc = Vco.

Question 19

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

Accepted Answer

The answer of With a base of n sides of...

Question 20

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

Accepted Answer

The answer of In the form  , verify Euler's...

Quiz 10: Surfaces and Solids

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.

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

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.

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.

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

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

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?

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

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.

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.

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

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.

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?

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?

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

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

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

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

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