Question

v = b · h
cylinder
h = 10
r = 4 cm

Explanation:

Step1: Recall the volume formula for a cylinder

The volume \( V \) of a cylinder is given by \( V = B \cdot H \), where \( B \) is the area of the base (a circle) and \( H \) (or \( h \)) is the height. The area of the circular base \( B=\pi r^{2} \), where \( r \) is the radius of the base.

Step2: Identify the given values

We are given that the radius \( r = 4\space cm \) and the height \( h=10\space cm \). First, calculate the area of the base \( B \):
\( B=\pi r^{2}=\pi\times(4)^{2}=\pi\times16 = 16\pi\space cm^{2} \)

Step3: Calculate the volume of the cylinder

Now, use the volume formula \( V = B\cdot h \). Substitute \( B = 16\pi \) and \( h = 10 \):
\( V=16\pi\times10=160\pi\space cm^{3} \)
If we take \( \pi\approx3.14 \), then \( V\approx160\times3.14 = 502.4\space cm^{3} \)

Answer:

The volume of the cylinder is \( 160\pi\space cm^{3} \) (or approximately \( 502.4\space cm^{3} \))