Geometry - Pre-Algebra
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A pyramid has height 4 feet. Its base is a square with sidelength 3 feet. Give its volume in cubic inches.
A pyramid has height 4 feet. Its base is a square with sidelength 3 feet. Give its volume in cubic inches.
Convert each measurement from inches to feet by multiplying it by 12:
Height: 4 feet =
inches
Sidelength of the base: 3 feet =
inches
The volume of a pyramid is

Since the base is a square, we can replace
:

Substitute 


The pyramid has volume 20,736 cubic inches.
Convert each measurement from inches to feet by multiplying it by 12:
Height: 4 feet = inches
Sidelength of the base: 3 feet = inches
The volume of a pyramid is
Since the base is a square, we can replace :
Substitute
The pyramid has volume 20,736 cubic inches.
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The height of a right pyramid is
feet. Its base is a square with sidelength
feet. Give its volume in cubic inches.
The height of a right pyramid is feet. Its base is a square with sidelength
feet. Give its volume in cubic inches.
Convert each of the measurements from feet to inches by multiplying by
.
Height:
inches
Sidelength of base:
inches
The base of the pyramid has area
square inches.
Substitute
into the volume formula:

cubic inches
Convert each of the measurements from feet to inches by multiplying by .
Height: inches
Sidelength of base: inches
The base of the pyramid has area
square inches.
Substitute into the volume formula:
cubic inches
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The height of a right pyramid and the sidelength of its square base are equal. The perimeter of the base is 3 feet. Give its volume in cubic inches.
The height of a right pyramid and the sidelength of its square base are equal. The perimeter of the base is 3 feet. Give its volume in cubic inches.
The perimeter of the square base,
feet, is equivalent to
inches; divide by
to get the sidelength of the base - and the height:
inches.
The area of the base is therefore
square inches.
In the formula for the volume of a pyramid, substitute
:
cubic inches.
The perimeter of the square base, feet, is equivalent to
inches; divide by
to get the sidelength of the base - and the height:
inches.
The area of the base is therefore square inches.
In the formula for the volume of a pyramid, substitute :
cubic inches.
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What is the volume of a pyramid with the following measurements?

What is the volume of a pyramid with the following measurements?
The volume of a pyramid can be determined using the following equation:

The volume of a pyramid can be determined using the following equation:
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Principal O'Shaughnessy has a paperweight in the shape of a pyramid with a square base. If one side of the base has a length of 4cm and the height of the paperweight is 6cm, what is the volume of the paperweight?
Principal O'Shaughnessy has a paperweight in the shape of a pyramid with a square base. If one side of the base has a length of 4cm and the height of the paperweight is 6cm, what is the volume of the paperweight?
We begin by recalling the volume of a pyramid.

where
is the area of the base and
is the height.
Since the base is a square, we can find the area by squaring the length of one of the sides.

Given the height is 6cm, we can now calculate the volume.

Since all of the measurements were in centimeters, our volume will be in cubic centimeters.
Therefore, the volume of Principal O'Shaughnessy's paperweight is
.
We begin by recalling the volume of a pyramid.
where is the area of the base and
is the height.
Since the base is a square, we can find the area by squaring the length of one of the sides.
Given the height is 6cm, we can now calculate the volume.
Since all of the measurements were in centimeters, our volume will be in cubic centimeters.
Therefore, the volume of Principal O'Shaughnessy's paperweight is .
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The volume of a square pyramid is
. If a side of the square base measures
. What is the height of the pyramid?
The volume of a square pyramid is . If a side of the square base measures
. What is the height of the pyramid?
The formula for the volume of a pyramid is
, where
is the area of the base and
is the height.
Using this formula,
= Area of the base, which is nothing but area of square with side
. 
Now,
when simplified, you get
.
Hence, the height of the pyramid is
.
The formula for the volume of a pyramid is , where
is the area of the base and
is the height.
Using this formula,
= Area of the base, which is nothing but area of square with side
.
Now, when simplified, you get
.
Hence, the height of the pyramid is .
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The pyramid has a length, width, and height of
respectively. What is the volume of the pyramid?
The pyramid has a length, width, and height of respectively. What is the volume of the pyramid?
Write the formula for the volume of a pyramid.

Substitute the dimensions and solve.

Write the formula for the volume of a pyramid.
Substitute the dimensions and solve.
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If the base area of the pyramid is
, and the height is
, what is the volume of the pyramid?
If the base area of the pyramid is , and the height is
, what is the volume of the pyramid?
Write the volume formula for the pyramid.

The base area is represented by
.
Substitute the knowns into the formula.

Write the volume formula for the pyramid.
The base area is represented by .
Substitute the knowns into the formula.
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Find the volume of a pyramid with a length of 4, width of 7, and a height of 3.
Find the volume of a pyramid with a length of 4, width of 7, and a height of 3.
Write the formula to find the area of a pyramid.

Substitute the dimensions.

Write the formula to find the area of a pyramid.
Substitute the dimensions.
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Find the volume of a pyramid if the length, base, and height are
respectively.
Find the volume of a pyramid if the length, base, and height are respectively.
Write the formula for the volume of a pyramid.

Substitute the dimensions and solve for the volume.

Write the formula for the volume of a pyramid.
Substitute the dimensions and solve for the volume.
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Find the volume of a pyramid with a length of 2, width of 6, and a height of 9.
Find the volume of a pyramid with a length of 2, width of 6, and a height of 9.
Write the formula for the volume of a pyramid.

Substitute the given length, width, and height.

Rewrite the
inside the parentheses as a factor of
.

Cancel the fraction with the three and multiply the terms to get the volume.

Write the formula for the volume of a pyramid.
Substitute the given length, width, and height.
Rewrite the inside the parentheses as a factor of
.
Cancel the fraction with the three and multiply the terms to get the volume.
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Find the volume of a pyramid if the dimensions of the length, width, and height are
, respectively.
Find the volume of a pyramid if the dimensions of the length, width, and height are , respectively.
Write the volume formula for a pyramid.

Plug in the dimensions.

Cancel out the three on the numerator and denominator.

Multiply.

Write the volume formula for a pyramid.
Plug in the dimensions.
Cancel out the three on the numerator and denominator.
Multiply.
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Find the volume of a pyramid with a length of 6cm, a width that is half the length, and a height that is two times the length.
Find the volume of a pyramid with a length of 6cm, a width that is half the length, and a height that is two times the length.
The formula for volume of a pyramid is

where l is the length, w is the width, and h is the height. We know the length is 6cm. The width is half the length, so the width is 3cm. The height is two times the length, so the height is 12cm. Using this information, we substitute. We get


The formula for volume of a pyramid is
where l is the length, w is the width, and h is the height. We know the length is 6cm. The width is half the length, so the width is 3cm. The height is two times the length, so the height is 12cm. Using this information, we substitute. We get
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The volume of a cone whose height is three times the radius of its base is one cubic yard. Give its radius in inches.
The volume of a cone whose height is three times the radius of its base is one cubic yard. Give its radius in inches.
The volume of a cone with base radius
and height
is

The height
is three times this, or
. Therefore, the formula becomes


Set this volume equal to one and solve for
:



![r=\sqrt[3]{\frac{ 1 }{ \pi}} ={\frac{ \sqrt[3] {1} }{ \sqrt[3]{ \pi}}} ={\frac{ 1}{ \sqrt[3]{ \pi}}}={\frac{1 \cdot \sqrt[3]{ \pi^{2} }}{ \sqrt[3]{ \pi} \cdot \sqrt[3]{ \pi^{2}}} ={\frac{ \sqrt[3]{ \pi^{2} }}{ \pi}}](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/204806/gif.latex)
This is the radius in yards; since the radius in inches is requested, multiply by 36.
![\frac{ \sqrt[3]{ \pi^{2} }}{ \pi} \times 36 = \frac{ 36 \sqrt[3]{ \pi^{2} }}{ \pi}](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/204807/gif.latex)
The volume of a cone with base radius and height
is
The height is three times this, or
. Therefore, the formula becomes
Set this volume equal to one and solve for :
This is the radius in yards; since the radius in inches is requested, multiply by 36.
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Which of the following is the volume of the above cone?
Which of the following is the volume of the above cone?
The volume of a cone whose height is
and whose base has radius
is defined by the formula
.
Set
:



cubic centimeters.
The volume of a cone whose height is and whose base has radius
is defined by the formula
.
Set :
cubic centimeters.
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You have an ice cream cone. You want to fill the cone completely with ice cream. What is the volume of ice cream you can fill it with if the height of the cone is 12cm and the diameter is 8cm?
You have an ice cream cone. You want to fill the cone completely with ice cream. What is the volume of ice cream you can fill it with if the height of the cone is 12cm and the diameter is 8cm?
The formula to find the volume of a cone is

where r is the radius and h is the height. We know the diameter of the ice cream cone is 8cm. We also know the radius is half the diameter, so the radius is 4cm. We know the height is 12cm. Using substitution, we get




The formula to find the volume of a cone is
where r is the radius and h is the height. We know the diameter of the ice cream cone is 8cm. We also know the radius is half the diameter, so the radius is 4cm. We know the height is 12cm. Using substitution, we get
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The standard waffle cone at Cream Canyon Ice Cream Parlor has a diameter of 4 inches. If the height of the cone is 1.5 times the diameter, what is the volume of the cone?
The standard waffle cone at Cream Canyon Ice Cream Parlor has a diameter of 4 inches. If the height of the cone is 1.5 times the diameter, what is the volume of the cone?
We must first recall the formula for the volume of a cone.

where
is the radius and
is the height. The problem is that we are not provided with either the height or the radius. However, we are told that the height is 1.5 times the diameter. Since the diameter is 4 inches, we can calculate
. Thus the height of the cone is 6 inches. We must also recall that the radius of a circle (such as the top of an ice cream cone) is simply half the diameter. Therefore, if the diameter is 4 inches, the radius is 2 inches. We now have all of the essential ingredients for volume.

Since our measurements were all in inches, our volume will be in cubic inches. Therefore, the volume of our ice cream cone is
. Now all we need is a scoop or two of our favorite flavor.
We must first recall the formula for the volume of a cone.
where is the radius and
is the height. The problem is that we are not provided with either the height or the radius. However, we are told that the height is 1.5 times the diameter. Since the diameter is 4 inches, we can calculate
. Thus the height of the cone is 6 inches. We must also recall that the radius of a circle (such as the top of an ice cream cone) is simply half the diameter. Therefore, if the diameter is 4 inches, the radius is 2 inches. We now have all of the essential ingredients for volume.
Since our measurements were all in inches, our volume will be in cubic inches. Therefore, the volume of our ice cream cone is . Now all we need is a scoop or two of our favorite flavor.
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What is the volume of a cone with a radius of two and a height of three?
What is the volume of a cone with a radius of two and a height of three?
Write the formula to find the volume of the cone.

Substitute the radius and height.

Write the formula to find the volume of the cone.
Substitute the radius and height.
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What is the volume of a cone with a radius of 5 and a height of 6?
What is the volume of a cone with a radius of 5 and a height of 6?
Write the formula to find the volume of a cone.

Substitute the dimensions and solve.

Write the formula to find the volume of a cone.
Substitute the dimensions and solve.
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Find the volume of a cone with a base area of
and a height of
.
Find the volume of a cone with a base area of and a height of
.
The base of a cone has a circular cross section. Given the base area, there is no need to determine the radius.
Write the formula for the volume of a cone.

The
term represents the base area of the circle.
Substitute all the given values into the volume formula.

The base of a cone has a circular cross section. Given the base area, there is no need to determine the radius.
Write the formula for the volume of a cone.
The term represents the base area of the circle.
Substitute all the given values into the volume formula.
Compare your answer with the correct one above