Question

given that the ( v = 450 , \text{m}^3 ) and the ( h = 15.2 , \text{m} ) find the radius of the cylinder, rounded to the nearest tenth. use ( pi approx 3.14 ) in all calculations:

a 1.9 m
b 3.1 m
c 9.4 m
d 29.6 m

Explanation:

Step1: Recall the volume formula for a cylinder

The volume \( V \) of a cylinder is given by the formula \( V=\pi r^{2}h \), where \( r \) is the radius and \( h \) is the height. We are given \( V = 450\space m^{3}\), \( h=15.2\space m \) and \( \pi\approx3.14 \). We need to solve for \( r \).

First, we can rearrange the formula to solve for \( r^{2} \):

$$ r^{2}=\frac{V}{\pi h} $$

Step2: Substitute the given values into the formula for \( r^{2} \)

Substitute \( V = 450 \), \( h = 15.2 \) and \( \pi\approx3.14 \) into the formula:

$$ r^{2}=\frac{450}{3.14\times15.2} $$

First, calculate the denominator: \( 3.14\times15.2 = 3.14\times15+3.14\times0.2=47.1 + 0.628 = 47.728 \)

Then, calculate \( r^{2} \): \( r^{2}=\frac{450}{47.728}\approx9.428 \)

Step3: Solve for \( r \)

Take the square root of both sides to find \( r \):

$$ r=\sqrt{9.428}\approx3.1 $$

(rounded to the nearest tenth)

Answer:

B. 3.1 m