Question

consider this cylinder. use the formula for the volume of a cylinder to answer the questions. cylinder ( v = bh ) what is the area of the base of the cylinder? ( pi mathrm{cm}^{2} ) what is the volume of the cylinder? ( pi mathrm{cm}^{3} )

Explanation:

Step1: Calculate the area of the base

The base of a cylinder is a circle. The formula for the area of a circle is \( B=\pi r^{2} \). Given the radius \( r = 5\space cm \), then \( B=\pi\times5^{2}=25\pi\space cm^{2} \).

Step2: Calculate the volume of the cylinder

The formula for the volume of a cylinder is \( V = Bh \). We know \( B = 25\pi\space cm^{2} \) and \( h=12.5\space cm \). Substitute the values into the formula: \( V=25\pi\times12.5 = 312.5\pi\space cm^{3} \).

Answer:

The area of the base is \( 25\pi\space cm^{2} \) and the volume of the cylinder is \( 312.5\pi\space cm^{3} \).