Question

question 27 of 50
what is the volume of a cylinder with a height of 12 units and a base diameter of 10 units?
○ 768 units cubed
○ 1,256 units cubed
○ 942 units cubed

Explanation:

Step1: Recall the formula for the volume of a cylinder

The formula for the volume \( V \) of a cylinder is \( V=\pi r^{2}h \), where \( r \) is the radius of the base and \( h \) is the height of the cylinder.

Step2: Find the radius from the diameter

Given that the diameter \( d = 10 \) units, the radius \( r=\frac{d}{2}=\frac{10}{2} = 5 \) units. The height \( h = 12 \) units.

Step3: Substitute the values into the formula

Substitute \( r = 5 \) and \( h=12 \) into the formula \( V=\pi r^{2}h \). We get \( V=\pi\times(5)^{2}\times12 \). First, calculate \( 5^{2}=25 \), then \( 25\times12 = 300 \). So \( V = 300\pi\). Taking \( \pi\approx3.14 \), we have \( V\approx300\times3.14=942 \) cubic units.

Answer:

942 units cubed