Question

what is the formula for the volume of a cylinder?
a. v = πd²
b. v = πr²h
c. v = l×w×h
d. v = 2πrh

a rectangular prism and a cylinder have equal volumes of 500 cm³. if the prisms height is 10 cm, what is the base area of the prism?
a. 10 cm²
b. 25 cm²
c. 100 cm²
d. 50 cm²

Explanation:

Step1: Recall volume formula for cylinder

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

Step2: Recall volume formula for rectangular - prism

The volume formula for a rectangular prism is $V = Bh$, where $B$ is the base - area and $h$ is the height. Given $V = 500\ cm^{3}$ and $h = 10\ cm$. We can find $B$ by rearranging the formula $B=\frac{V}{h}$.

Step3: Calculate base - area of rectangular prism

Substitute $V = 500\ cm^{3}$ and $h = 10\ cm$ into $B=\frac{V}{h}$. So $B=\frac{500}{10}=50\ cm^{2}$.

Answer:

1. B. $V=\pi r^{2}h$
2. D. $50\ cm^{2}$