VOLUME OF PYRAMID WORKSHEET

Find the volume of the pyramid :

Question 1 :

Question 2 :

Question 3 :

Question 4 :

Question 5 :

a. The volume of sunscreen in Bottle B is about how many times the volume in Bottle A?

b. Which is the better buy?

Question 6 :

Which sand-castle spire has a greater volume? How much more sand do you need to make the spire with the greater volume?

Question 7 :

How much glass is needed to manufacture 1000 paperweights? Explain your reasoning.

Question 8 :

Use the photo of the tepee.

a. What is the shape of the base? How can you tell?

b. The tepee’s height is about 10 feet. Estimate the volume of the tepee

Question 9 :

A pyramid hip roof is a good choice for a house in a hurricane area. What is the volume of the roof to the nearest tenth?

Question 10 :

Lynette has a metal doorstop with the dimensions shown. Each cubic centimeter of the metal in the doorstop has a mass of about 8.6 grams. Find the volume of the metal in the doorstop. Then find the mass of the doorstop.

1. Answer :

Formula to find volume of pyramid is

=  (1/3) x Base area x Height

Here, the base is a square with side length 8 cm. 

So, area of the base is 

=  8 x 8

=  64 cm²

Height of the pyramid is 9 cm.

Then, volume of the pyramid is 

=  (1/3) x 64 x 9

=  192 cm³

2. Answer :

Formula to find volume of pyramid is

=  (1/3) x Base area x Height

Here, the base is a rectangle with side length 10 inches and width 8 inches.  

So, area of the base is

=  10 x 8

=  80 in²

Height of the pyramid is 6 inches.

Then, volume of the pyramid is

=  (1/3) x 80 x 6

=  160 in³

3. Answer :

Formula to find volume of pyramid is

=  (1/3) x Base area x Height

Here, the base is an equilateral triangle with side length of 8 cm.

So, area of the base is

=  (√3 / 4) x 8²

=  16√3 cm²

Height of the pyramid is 10 cm.

Then, volume of the pyramid  is

=  (1/3) x (16√3) x 10

=  160√3 / 3 cm³

4. Answer :

Formula to find volume of pyramid is

=  (1/3) x Base area x Height

Here, the base is a triangle with height 7 inches and base 8 inches.

So, area of the base is 

=  (1/2) x 8 x 7

=  28 in²

Height of the pyramid is 9 inches.

Then, volume of the pyramid is 

=  (1/3) x 28 x 9

=  84 in³

5. Answer :

a)  Use the formula for the volume of a pyramid to estimate the amount of sunscreen in each bottle.

Measrues of bottle A :

Length = 2 inches, width = 1 inch and height = 6 inches

Quantity of sunscreen in bottle A

= (1/3) x base area x height

= (1/3) x 2 x 1 x 6

= 4 cubic inches

Measrues of bottle B :

Length = 3 inches, width = 1.5 inches and height = 4 inches

Quantity of sunscreen in bottle B

= (1/3) x base area x height

= (1/3) x 3 x 1.5 x 4

= 6 cubic inches

Volume of sunscreen in bottle B / Volume of sunscreen in bottle A

= 6/4

= 1.5

So, quantity of sunscreen in bottle B is 1.5 times of bottle A.

b) Unit cost of bottle A :

Cost of bottle A = $9.96

Cost of 1 inch = 9.96/4

= $2.49

Unit cost of bottle B :

Cost of bottle B = $14.40

Cost of 1 inch = 14.40/6

= $2.4

The unit cost of Bottle B is less than the unit cost of Bottle A. So, Bottle B is the better buy

6. Answer :

Volume of spire A = base area x height

= 30 x 6

= 180 square inches

Volume of spire B = 24 x 8

= 192 square inches

So, Spire B has greater volume.

7. Answer :

Volume of one paper weight = base area x height

= 3 x 3 x 4

= 36 cubic inches

To make 100 paper weight, quantity of glass needed

= 100 x 36

= 3600 cubic inches

8. Answer :

a) The base looks like a circle and its radius is 5 cm

b) Volume = (1/3) x 3.14 x 5² x 10

= (1/3) x 3.14 x 25 x 10

= 261.6 cubic cm

9. Answer :

Area of square base = 40 x 40

= 1600 square feet

height of roof = 20 ft

Volume of material required for roof = 1600 x 20

= 32000 cubic feet.

10. Answer :

Volume = base area x height

area of rectangle = 10 x 2.5

= 25 cm²

Volume = 25 x 6

= 150 cm³

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