Problem 8
The box portion of the shed (ignoring the triangular roof) has a volume of:
length*width*height = 10*8*6.5 = 520 cubic feet
The triangular face on the right side has an area of base*height/2 = 8*2.5/2 = 10. Multiply this with the depth of the triangular prism and we get a volume of 10*10 = 100 cubic feet.
The two sub-volumes combine to 520+100 = 620
Answer: 620 cubic feet
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Problem 9
Let's find the area of the base
area = side*side = (4.2)*(4.2) = 17.64 sq inches
Then we plug that into the formula below, along with the height of the pyramid
V = volume of a pyramid
V = (1/3)*(area of the base)*(height)
V = (1/3)*(17.64)*(5)
V = 29.4
Answer: 29.4 cubic inches
Your teacher made a typo. She or he should have written [tex]\text{in}^3[/tex] instead of [tex]\text{in}^2[/tex]
