Question

What is the volume of the composite figure? 12in 4 in 3 in. 7 in.

Answer 1

Answer:

Step-by-step explanation:

$V_p = b \cdot h \cdot w$, where b, h, w are base, height and width respectively.

$V_{sp} = \frac{1}{3} \cdot {A_b} \cdot h$, where h is the height, and A_b is the area of the base.

First let's calculate the volume of the paralelipiped by the first formula.

$V_p = 7 \cdot 4 \cdot 3 = 84 in^2$

Then let's find out the height of the pyramid, which is 12 - 4 = 8 in.(See drawing)

Then the area of the base of the square pyramid is simply.

$A_r = 3 \cdot 7 = 21 in^2$

Now we can find the volume of the pyramid.

$V_{sp} = \frac{1}{3} \cdot 21 \cdot 8 = 56 in^3$

To find the total volume, let's add both volumes.

$V_T = 84 + 56 = 140 in^3$