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Learning Diagnostic Analytics GA Recommendations Math Pa Skill plans Social studies Language arts Science Eighth grade > T.11 Volume of cones YYR A cone has a volume of 602.88 cubic centimeters and a height of 16 centimeters. What is its radius? Use 3.14 and round your answer to the nearest hundredth. centimeters Submit

Sagot :

Answer:

6cm

Explanation:

The below formula can be used to determine the volume of a cone;

[tex]V=\pi\times r^2\times\frac{h}{3}[/tex]

Given V which is the volume of the cone as 602.88cm^3 and the height(h) as 16cm, let's go ahead and solve for radius(r) using the below steps;

Multiply both sides by 3;

[tex]3V=\pi\times r^2\times h[/tex]

Divide both sides by the product of pi and h;

[tex]\frac{3V}{\pi h}=r^2[/tex]

Take the square root of both sides;

[tex]r=\sqrt[]{\frac{3V}{\pi h}}[/tex]

Substitute the given values and solve for r;

[tex]r=\sqrt[]{\frac{3\times602.88}{3.14\times16}}=\sqrt[]{\frac{1808.64}{50.24}}=6\operatorname{cm}[/tex]

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