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Alex_Xolod [135]
2 years ago
15

A conical tent has a radius of 10.4 ft and a height of 8.4 ft. Doubling which dimensions will quadruple the volume of the tent?

Mathematics
1 answer:
avanturin [10]2 years ago
5 0

Answer: Doubling the radius.

Step-by-step explanation:

The volume of a cone can be found with the following formula:

V=\frac{1}{3}\pi r^2h

Where "r" is the radius and "h" is the height of the cone.

Let's find the volume of the conical tent with a radius of 10.4 feet and a height of 8.4 feet.

Identifiying that:

r=10.4\ ft\\\\h=8.4\ ft

You get this volume:

V_1=\frac{1}{3}\pi (10.4\ ft)^2(8.4\ ft)\\\\V_1=951.43\ ft^3

If you double the radius, the volume of the conical tent will be:

V_2=\frac{1}{3}\pi (2*10.4\ ft)^2(8.4\ ft)\\\\V_2=3,805.70\ ft^3

When you divide both volumes, you get:

\frac{3,805.70\ ft^3}{951.43\ ft^3}=4

Therefore, doubling the radius will quadruple the volume of the tent.

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