Question

spaghetti sauce comes in large and small cylindrical cans. the larger can has a radius and height that are both three times longer than the radius and height of the smaller can. if the volume of the smaller can is 35.28 in³, what is the volume of the larger can?

a. 211.68 in³
b. 105.84 in³
c. 952.56 in³
d. 317.52 in³

Explanation:

Step1: Recall the volume formula for a cylinder

The volume formula of a cylinder is $V = \pi r^{2}h$. Let the radius of the smaller - can be $r_1$ and height be $h_1$, so its volume $V_1=\pi r_1^{2}h_1 = 35.28$ in³. The radius of the larger can is $r_2 = 3r_1$ and the height is $h_2 = 3h_1$.

Step2: Calculate the volume of the larger can

The volume of the larger can $V_2=\pi r_2^{2}h_2$. Substitute $r_2 = 3r_1$ and $h_2 = 3h_1$ into the formula: $V_2=\pi(3r_1)^{2}(3h_1)=\pi\times9r_1^{2}\times3h_1 = 27\pi r_1^{2}h_1$.

Step3: Substitute the value of $V_1$

Since $V_1=\pi r_1^{2}h_1 = 35.28$ in³, then $V_2 = 27V_1$.
$V_2=27\times35.28=952.56$ in³.

Answer:

C. $952.56$ in³