CK-12 Geometry Concepts

11.8. Composite Solids http://www.ck12.org

3. Using your work from #2, find the volume of the pyramid and then of the entire solid.

Answers:

1. This is a square prism with a square pyramid on top. Find the volume of each separeatly and then add them
   together to find the total volume. First, we need to find the height of the pyramid portion. The slant height is 25
   and the edge is 48. Using have of the edge, we have a right triangle and we can use the Pythagorean Theorem.
   h=

√

252 − 242 = 7

Vprism= ( 48 )( 48 )( 18 ) = 41472 cm^3

Vpyramid=

1

3

( 482 )( 7 ) = 5376 cm^3

The total volume is 41472+ 5376 = 46 , 848 cm^3.

2. Use what you know about prisms.

Vprism=B·h

Vprism= ( 4 · 4 )· 5

Vprism= 80 in^3

3. Use what you know about pyramids.

Vpyramid=

1

3

B·h

Vpyramid=

1

3

( 4 · 4 )( 6 )

Vpyramid= 32 in^3

Now find the total volume by finding the sum of the volumes of each solid.

Vtotal=Vprism+Vpyramid

Vtotal= 112 in^3

Practice

Find the volume of the composite solids below. Round your answers to the nearest hundredth.

1. The bases are squares. Find the volume of the green part.


2. 
   


3. A cylinder fits tightly inside a rectangular prism with dimensions in the ratio 5:5:7 and volume 1400in^3. Find
   the volume of the space inside the prism that is not contained in the cylinder.

Find the surface area and volume of the following shapes. Leave your answers in terms ofπ.

4.

5.