Question

a cylinder has a radius of 3 cm and a height of 10 cm. if the length of the radius is increased by 10%, but its height doesnt change, by how many cubic centimeters does the volume of the cylinder increase? (use 3.14 for π)
a. 341.946 cm³
b. 282.6 cm³
c. 103.62 cm³
d. 59.346 cm³

Explanation:

Step1: Calculate original volume

The volume formula of a cylinder is $V = \pi r^{2}h$. Given $r = 3$ cm, $h=10$ cm and $\pi = 3.14$. So the original volume $V_1=3.14\times3^{2}\times10=3.14\times9\times 10 = 282.6$ $cm^{3}$.

Step2: Calculate new radius

The radius is increased by 10%. The new radius $r_2=3\times(1 + 0.1)=3\times1.1 = 3.3$ cm.

Step3: Calculate new volume

Using the volume formula $V=\pi r^{2}h$ with $r = r_2 = 3.3$ cm, $h = 10$ cm and $\pi=3.14$. So the new volume $V_2=3.14\times3.3^{2}\times10=3.14\times10.89\times10 = 341.946$ $cm^{3}$.

Step4: Calculate volume increase

The increase in volume $\Delta V=V_2 - V_1=341.946-282.6 = 59.346$ $cm^{3}$.

Answer:

D. $59.346$ $cm^{3}$