Question

a cone has a volume 1309 cm3 if the height of the cone is 8 centimeters find the radius

Answer 1

Answer:

r = 12.5 (1 d.p.)

Step-by-step explanation:

The volume of a cone is given by:

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

We are given V and h. Sub these numbers into their respective variables,

$1309=\frac{1}{3} \pi r^{2} (8)$

Simplify,

$3927=8\pi r^{2}$

$\frac{3927}{8} =\pi r^{2}$

$\frac{3927}{8\pi } =r^{2}$

r = $\sqrt{\frac{3927}{8\pi } }$

r = 12.5 (1 d.p.)

Answer 2

The radius of the cone is 12.50 cm.

It is given that a cone has a volume of 1309 cm3 if the height of the cone is 8 centimeters.

It is required to find the radius of the cone.

What is volume?

It is defined as a three-dimensional space enclosed by an object or thing.

We know the volume of a cone:

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

We have V = 1309 cubic cm

And h = 8 centimeters

$\rm 1309 = \pi r^2\frac{8}{3}$

$\rm 1309 \times 3(\frac{1}{8} )= \pi r^2$

$\rm 490.875= \pi r^2$  or

$\rm r^2 = \frac{490.875}{\pi}$

$\rm r = \sqrt{156.25} \\\\\rm r = 12.50 cm$

Thus, the radius of the cone is 12.50 cm.

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