Question

question 3 1 point a prism has a height of 5 inches and a volume of 80 cubic inches. select all figures that could be the base for this prism. a. a square with side length 4 inches. b. a 2 - inch - by - 8 - inch rectangle c. a circle with radius 2 inches d. a right triangle with legs 4 inches long e. a heart - shaped base with an area of 16 square inches

Explanation:

Step1: Recall prism - volume formula

The volume formula of a prism is $V = Bh$, where $B$ is the area of the base and $h$ is the height. Given $V = 80$ cubic inches and $h=5$ inches, we can find $B$ by rearranging the formula: $B=\frac{V}{h}$.

Step2: Calculate the base - area

Substitute $V = 80$ and $h = 5$ into the formula $B=\frac{V}{h}$. We get $B=\frac{80}{5}=16$ square inches.

Step3: Calculate the area of each base - candidate

For option a:

The area of a square with side length $s = 4$ inches is $A=s^{2}=4^{2}=16$ square inches.

For option b:

The area of a rectangle with length $l = 8$ inches and width $w = 2$ inches is $A=lw=8\times2 = 16$ square inches.

For option c:

The area of a circle with radius $r = 2$ inches is $A=\pi r^{2}=\pi\times2^{2}=4\pi\approx12.56$ square inches.

For option d:

The area of a right - triangle with legs $a = 4$ inches and $b = 4$ inches is $A=\frac{1}{2}ab=\frac{1}{2}\times4\times4 = 8$ square inches.

For option e:

The area of the heart - shaped base is given as 16 square inches.

Answer:

a. A square with side length 4 inches.
b. A 2 - inch - by - 8 - inch rectangle.
e. A heart - shaped base with an area of 16 square inches.