Question

a soccer team uses cones to outline their field in practices. the volume of each of the cones is 1.05 liters. the height of each cone is equal to 3 times the radius of the base. find the radius of the cones in centimeters, rounded to the nearest hundredth. (note: 1 l = 1000 cm³)
enter the correct value in the box.
show hints
the radius of the base of the cone is about centimeters.
7 8 9 +
4 5 6 -
1 2 3 ×

Explanation:

Step1: Convert volume to \(cm^{3}\)

Given \(1L = 1000cm^{3}\), so \(V=1.05L = 1.05\times1000 = 1050cm^{3}\)

Step2: Express height in terms of radius

Let radius be \(r\), then height \(h = 3r\)

Step3: Use cone volume formula \(V=\frac{1}{3}\pi r^{2}h\)

Substitute \(h = 3r\) into formula: \(V=\frac{1}{3}\pi r^{2}(3r)=\pi r^{3}\)

Step4: Solve for \(r\)

Since \(V = 1050=\pi r^{3}\), then \(r^{3}=\frac{1050}{\pi}\approx\frac{1050}{3.14}\approx334.4\)
\(r=\sqrt[3]{334.4}\approx6.94\)

Answer:

\(6.94\)