Question

question 29 of 39
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. 952.56 in³
b. 317.52 in³
c. 211.68 in³
d. 105.84 in³

Explanation:

Step1: Recall the volume formula for a cylinder

The volume formula for a cylinder is \(V = \pi r^{2}h\).

Step2: Analyze the ratio of dimensions

Let the radius of the smaller can be \(r\) and height be \(h\). For the larger can, radius \(R = 3r\) and height \(H=3h\).

Step3: Calculate the volume of the larger can in terms of the smaller can

The volume of the smaller can \(V_{s}=\pi r^{2}h = 35.28\). The volume of the larger can \(V_{l}=\pi R^{2}H=\pi(3r)^{2}(3h)=27\pi r^{2}h\).

Step4: Substitute the value of the smaller can's volume

Since \(\pi r^{2}h = 35.28\), then \(V_{l}=27\times35.28 = 952.56\).

Answer:

A. \(952.56\ \text{in}^3\)