Question

4.7 volume of prisms and cylinders
find the volume or each triangular prism. formula: v = bh or v = ½bhh
a. 7 feet 8 feet 10 feet
b. 3 in 4 in 5 in 8 in
c.
a. □ ft³
b. □ in³
c. □ units³

Explanation:

Step1: Calculate base - area for part a

For the triangular base of the prism in part a, with base of the triangle $b = 8$ feet and height of the triangle $h=7$ feet. The area of the triangular base $B=\frac{1}{2}bh$. So, $B=\frac{1}{2}\times8\times7 = 28$ square - feet. The height of the prism $H = 10$ feet. Using the volume formula $V=BH$, we get $V=28\times10=280$ cubic - feet.

Step2: Calculate base - area for part b

For the triangular base of the prism in part b, with $b = 4$ inches and $h = 3$ inches. The area of the triangular base $B=\frac{1}{2}bh=\frac{1}{2}\times4\times3=6$ square inches. The height of the prism $H = 8$ inches. Using the volume formula $V = BH$, we get $V=6\times8 = 48$ cubic inches.

Step3: Calculate base - area for part c

For the triangular base of the prism in part c, with $b = 8$ and $h = 4$. The area of the triangular base $B=\frac{1}{2}bh=\frac{1}{2}\times8\times4 = 16$. The height of the prism $H = 14$. Using the volume formula $V=BH$, we get $V=16\times14=224$ cubic units.

Answer:

a. $280$
b. $48$
c. $224$