Question

The surface area of a sphere is same as the curved surface area of a right circular cylinder, whose height and diameter are 12 cm each. The radius of sphere is ___cm.
(a) 3
(b) 4
(c) 6
(d) 12

Answer 1

Answer:

Radius of sphere is 6 cm.

Option C is the correct answer.

Step-by-step explanation:

Surface area of sphere:

$S_{sphere}= 4\pi \: {r}^{2}$

Curved surface area of right circular cylinder:

$CSA_{cylinder}= 2\pi \: r \: h \\ \\ r = 6 \: cm \\ \\ h = 12 \: \: cm \\ \\ CSA_{cylinder}= 2 \times \pi \times 6 \times 12 \\ \\ CSA_{cylinder} = \pi \times 144 \: {cm}^{2}$

As surface area of a sphere is same as the curved surface area of a right circular cylinder, so

$4\pi \: {r}^{2} = \pi \: \times 144 \\ \\ {r}^{2} = \frac{144}{4} \\ \\ {r}^{2} = 36 \\ \\ r = 6 \: cm$

Radius of sphere is 6 cm.

Option C is the correct answer.

Hope it helps you.

Answer 2

• Height of the cylinder=12cm

• Diameter of cylinder =12 cm•

• radius= 12/2 =6 cm

Curved Surface area of sphere= Curved Surface Area of cylinder..

Now do it