Question

the height of a cylinder with a volume of 314 cm³ and a radius of 5 cm is ______. a. 15 cm b. 4 cm c. 5 cm d. 10 cm what is the volume of a cylinder with a radius of 2 and a height of 3? a. 37.68 b. 56.52 c. 18.84 d. 12.56

Explanation:

Step1: Recall volume formula for cylinder

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

Step2: Solve for height in first - question

Given $V = 314\ cm^{3}$, $r = 5\ cm$. Substitute into the formula: $314=\pi\times5^{2}\times h$. First, calculate $5^{2}=25$. Then the equation becomes $314=\pi\times25\times h$. Since $\pi\approx3.14$, we have $314 = 3.14\times25\times h$. $3.14\times25 = 78.5$, so $314=78.5h$. Solving for $h$, we get $h=\frac{314}{78.5}=4\ cm$.

Step3: Solve for volume in second - question

Given $r = 2$ and $h = 3$. Substitute into the formula $V=\pi r^{2}h$. So $V=3.14\times2^{2}\times3$. First, calculate $2^{2}=4$. Then $V=3.14\times4\times3=37.68$.

Answer:

1. b. 4 cm
2. a. 37.68