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  • The radius of a hemispherical balloon increases from 6 cm to 12 cm as air is being pumped into it. The ratios of the surface areas of the balloon in the two cases is: (A) 1:4 (B) 1:3 (C) 2:3 (D) 2:1

The radius of a hemispherical balloon increases from 6 cm \; to\; 12 cm as air is being pumped into it. The ratios of the surface areas of the balloon in the two cases is:

(A) 1:4

(B) 1:3

(C) 2:3

(D) 2:1

Answers (1)

Answer (A)

We know that for a hemisphere

Total surface area of =2\pi r^{2}+\pi r^{2}=3 \pi r^{2}                         ( Where r is the radius)

Now it is given that the radius of a hemispherical balloon increases from 6 cm to 12 cm

So,

When r=6, total surface area \left ( S_{1} \right )=3 \pi\left ( 6 \right )^{2}=36

When r=12, total surface area \left ( S_{2} \right )=3 \pi\left ( 12 \right )^{2}=144

Hence, required ratio=\left ( S_{1} \right ):\left ( S_{2} \right )

                                   =36 :144

                                    =1 : 4

So, option (A) is the correct answer.

Posted by

infoexpert23

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