Question

Mason built a model of a birdhouse for his engineering class, as pictured below.

Answer 1

Remember that

the volume of the figure is equal to the volume of the pyramid plus the volume of the rectangular prism

so

step 1

Find out the volume of the rectangular prism

V=L*W*H

substitute given values

V=(8)(8)(14)

V=896 in3

step 2

Find out the volume of pyramid

V=(1/3)Bh

where

B is the area of the square base

h is the height of the prism

Find out the height of pyramid

Applying Pythagorean Theorem

10^2=h^2+4^2

h^2=100-16

h^2=84

h=√84 in=2√21 in

Find the volume

V=(1/3)(8^2)(2√21)

V=(128/3)√21 in3

step 3

the total volume is

V=896+(128/3)√21 in3