Question

ellie just got a new drum set for her birthday. it includes a bass drum and a snare drum, both of which are shaped like cylinders. the bass drum has a volume of 5,026.55 cubic inches, which is 4 times the volume of the snare drum. if ellies snare drum has a height of 8 inches, what is its radius?
round your answer to the nearest hundredth.

inches

Explanation:

Step1: Calculate the volume of the snare drum

Since the bass drum's volume \(V_{bass}=5026.55\) cubic inches and \(V_{bass} = 4V_{snare}\), then \(V_{snare}=\frac{V_{bass}}{4}\).
\(V_{snare}=\frac{5026.55}{4}=1256.6375\) cubic inches.

Step2: Use the formula for the volume of a cylinder

The formula for the volume of a cylinder is \(V=\pi r^{2}h\), where \(V = 1256.6375\) cubic inches, \(h = 8\) inches, and \(\pi\approx3.14\).
Substitute the values into the formula: \(1256.6375=3.14\times r^{2}\times8\).
First, simplify the right - hand side: \(3.14\times8 = 25.12\). So the equation becomes \(1256.6375=25.12r^{2}\).
Then solve for \(r^{2}\): \(r^{2}=\frac{1256.6375}{25.12}\).
\(r^{2}=50.025378\).

Step3: Find the radius \(r\)

Take the square root of \(r^{2}\): \(r=\sqrt{50.025378}\).
\(r\approx7.07\) inches.

Answer:

\(7.07\) inches