Question

3 practice 3
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
how did i do?

Explanation:

Step1: Find required base area

The volume of a prism is $V = B \times h$, where $B$ is the base area and $h$ is the height. Rearrange to solve for $B$:
$B = \frac{V}{h} = \frac{80}{5} = 16$ square inches.
We need figures with base area = 16 square inches.

Step2: Calculate area of Option A

Area of square: $s^2$ where $s=4$.
$4^2 = 16$ square inches.

Step3: Calculate area of Option B

Area of rectangle: $l \times w$ where $l=8, w=2$.
$8 \times 2 = 16$ square inches.

Step4: Calculate area of Option C

Area of circle: $\pi r^2$ where $r=2$.
$\pi (2)^2 = 4\pi \approx 12.57$ square inches.

Step5: Calculate area of Option D

Area of right triangle: $\frac{1}{2} \times l_1 \times l_2$ where $l_1=l_2=4$.
$\frac{1}{2} \times 4 \times 4 = 8$ square inches.

Step6: Check area of Option E

Given area = 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