Question

the diagram shows a square pyramid over a cube. what is the volume of the entire figure?

Answer 1

Answer:

$1,233\frac{1}{3}\ in^3$

Step-by-step explanation:

The picture of the question in the attached figure

we know that

The volume of the figure is equal to the volume of the cube plus the volume of the square pyramid

Find the volume of the cube

$V=b^3$

where

b is the length side of the cube

we have

$b=10\ in$

$V=10^3=1,000\ in^3$

Find the volume of the square pyramid

$V=\frac{1}{3}b^{2}h$

where

b is the length side of the square base

h is the height of the pyramid

we have

$b=10\ in$

$h=17-10=7\ in$

substitute

$V=\frac{1}{3}(10)^{2}(7)$

$V=\frac{700}{3}\ in^3$

Find the volume of the complete figure

Adds the volumes

$V=1,000+\frac{700}{3}=\frac{3,700}{3}\ in^3$

convert to mixed number

$\frac{3,700}{3}\ in^3=\frac{3,699}{3}+\frac{1}{3}=1,233\frac{1}{3}\ in^3$