Question

for an art class, darnel is creating a model building shaped like a cylinder. he has 946 cubic centimeters of clay to work with and wants the diameter of his model building to be 12.5 centimeters. if darnel uses all of his clay, what will the height of his model building be? round your answer to the nearest hundredth. centimeters submit

Explanation:

Step1: Find the radius

The formula for the radius \(r\) of a circle is \(r=\frac{d}{2}\), where \(d\) is the diameter. Given \(d = 12.5\) cm, so \(r=\frac{12.5}{2}=6.25\) cm.

Step2: Use the volume formula of a cylinder

The volume formula of a cylinder is \(V=\pi r^{2}h\), where \(V\) is the volume, \(r\) is the radius and \(h\) is the height. We know \(V = 946\) \(cm^{3}\), \(r = 6.25\) cm and \(\pi\approx3.14\).
Substitute the values into the formula: \(946=3.14\times(6.25)^{2}\times h\).
First, calculate \((6.25)^{2}=6.25\times6.25 = 39.0625\). Then the equation becomes \(946=3.14\times39.0625\times h\).
Calculate \(3.14\times39.0625=122.65625\). So the equation is \(946 = 122.65625h\).

Step3: Solve for \(h\)

To find \(h\), use the formula \(h=\frac{V}{\pi r^{2}}\). So \(h=\frac{946}{122.65625}\).
\(h=\frac{946}{122.65625}\approx7.71\)

Answer:

\(7.71\)