Principal O"Shaughnessy has actually a paperweight in the form of a pyramid v a square base. If one next of the base has actually a length of 4cm and the elevation of the paperweight is 6cm, what is the volume of the paperweight?


*


*


*


*


*


Explanation:

We start by recalling the volume of a pyramid.

You are watching: Find the height of a square pyramid that has a volume of 32 cubic feet and a base length of 4 feet.

*
 

where 

*
 is the area of the base and 
*
 is the height.

Since the base is a square, us can discover the area through squaring the size of one of the sides.

*

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

*

Since every one of the measurements were in centimeters, ours volume will certainly be in cubic centimeters. 

Therefore, the volume of major O"Shaughnessy"s paperweight is 

*
.


The volume the a square pyramid is 

*
. If a next of the square basic measures 
*
. What is the elevation of the pyramid?


Explanation:

The formula for the volume the a pyramid is 

*
, wherein
*
 is the area the the base and
*
 is the height.

 Using this formula, 

*
 = Area of the base, which is nothing however area that square with side
*
*

Now, 

*
 when simplified, girlfriend get 
*
.

Hence, the height of the pyramid is 

*
.


A pyramid has height 4 feet. Its basic is a square v sidelength 3 feet. Give its volume in cubic inches.


Explanation:

Convert each measurement native inches to feet by multiplying it through 12:

Height: 4 feet = 

*
 inches

Sidelength of the base: 3 feet = 

*
 inches

The volume that a pyramid is 

*

Since the base is a square, we can replace 

*
:

*

Substitute 

*

*

*

The pyramid has volume 20,736 cubic inches.

 


The elevation of a ideal pyramid is 

*
feet. Its basic is a square with sidelength 
*
feet. Provide its volume in cubic inches.


Explanation:

Convert each of the measurements from feet to inches through multiplying by

*
.

Height: 

*
 inches

Sidelength the base: 

*
 inches

The basic of the pyramid has actually area 

*
 square inches.

Substitute 

*
into the volume formula:

*

*
 cubic inches


The elevation of a right pyramid and the sidelength the its square base are equal. The perimeter of the basic is 3 feet. Give its volume in cubic inches.


Explanation:

The perimeter of the square base, 

*
feet, is indistinguishable to 
*
 inches; divide by 
*
to acquire the sidelength that the base - and also the height: 
*
 inches. 

The area the the base is therefore 

*
 square inches. 

In the formula for the volume the a pyramid, substitute 

*
:

*
 cubic inches.


Explanation:

Write the volume formula for the pyramid.

*

The base area is represented by 

*
.

Substitute the knowns right into the formula.

*


Explanation:

Write the formula because that the volume the a pyramid.

*

Substitute the dimensions and solve because that the volume.

*


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