Question

The surface area of a sphere of radius 5 cm is five times the CSA of a cone of radius 4 cm. Find the height and volume of the cone.

Answer 1

Step-by-step explanation:

Given:-

RADIUS OF SPHERE:-5cm

RADIUS OF CONE:-4cm

curved surface area of cone=5(surface area of sphere)

$4\pi \: {r1}^{2} = 5(\pi \: r \: l)$

where, r1 is radius of sphere.

l is slant height of cone.

r is radius of cone.

$4 \times {5 }^{2} = 5 \times 4 \times l$

$4 \times 25 = 20 \times l$

$= > l = 5cm$

We know that from Pythagoras theorem,

${h}^{2} = {l}^{2} - {r}^{2}$

by inserting values given we get,

${h}^{2} = {5}^{2} - {4}^{2}$

$h = \sqrt{25 - 16}$

$= > h = \sqrt{9} = 3cm$

Now by formula of volume of cone we get,

$volume \: of \: cone \: = \frac{1}{3} \pi {r}^{2} h$

$= \frac{1}{3} ( \frac{22}{7} \times 4 \times 4 \times 3)$

$= \frac{35.2}{7}$

$= > 50.29 \: cm$

Hope it helps you.

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