Question

a can is in the shape of a right circular cylinder with an inner diameter of 7.5 centimeters and an inner height of 12.5 centimeters. the can is placed on its circular base, and 450 milliliters of juice is poured into the can. given that 1 milliliter is equivalent to 1 cubic centimeter, what is the height of the juice in the can to the nearest tenth of a centimeter?
a. 2.5 cm
b. 8.0 cm
c. 10.2 cm
d. 11.3 cm

Explanation:

Step1: Find the radius of the can

The inner - diameter $d = 7.5$ cm, so the radius $r=\frac{d}{2}=\frac{7.5}{2}=3.75$ cm.

Step2: Recall the volume formula for a cylinder

The volume formula of a cylinder is $V=\pi r^{2}h$, where $V$ is the volume, $r$ is the radius of the base, and $h$ is the height. We know that the volume of the juice $V = 450$ $cm^{3}$ (since 1 mL = 1 $cm^{3}$), and we want to find the height $h$ of the juice. Rearranging the formula for $h$, we get $h=\frac{V}{\pi r^{2}}$.

Step3: Substitute the values into the formula

Substitute $V = 450$ $cm^{3}$ and $r = 3.75$ cm into the formula $h=\frac{V}{\pi r^{2}}$. Then $h=\frac{450}{\pi\times(3.75)^{2}}=\frac{450}{\pi\times14.0625}$.
Calculate $\pi\times14.0625\approx3.14\times14.0625 = 44.15625$. Then $h=\frac{450}{44.15625}\approx10.2$ cm.

Answer:

C. 10.2 cm