Question

The radius of a spherical balloon increases from 6 cm to 12 cm as air is being pumped into it. Then what will be the ratio of surface areas of the original balloon to the resulting new balloon ???

Answer 1

Step-by-step explanation:

Surface area of a spherical balloon whose radius is 6 cm.

= 4π × 6 × 6 cm2

Surface area of a spherical balloon whose radius is 12 cm.

= 4π × 12 × 12 cm2

∴ Ration of surface areas = 4π × 6 × 6 / 4π × 12 × 12 = 1 / 4 = 1 : 4

Answer 2

GivEn:

• The radius of a spherical balloon increases from 6 cm to 12 cm.

To find:

• Ratio of surface areas of the original balloon to the resulting new balloon.

SoluTion:

According to question,

The radius of a spherical balloon increases from 6 cm to 12 cm as air is being pumped into it.

So,

• Let's $\sf r_1 = 6\;cm$

• Let's $\sf r_2 = 12\;cm$

We know that,

$\star\;{\boxed{\sf{\purple{Surface\;Area\;of\; hemisphere = 3 \pi r^2}}}}$

Therefore,

Ratio of surface areas of the original balloon to the resulting new balloon is,

⠀⠀⠀

$:\implies\sf \red{ \dfrac{Surface\;area\;of\; original\;balloon}{Surface\;area\;of\;new\;balloon}}$

⠀⠀⠀⠀⠀⠀⠀

$:\implies\sf \dfrac{3 \pi r_1}{3 \pi r_2}$

⠀⠀⠀

$:\implies\sf \dfrac{ \cancel{3 \times \pi} \times (6)^2}{ \cancel{3 \times \pi} \times (12)^2}$

⠀⠀⠀

$:\implies\sf \cancel{ \dfrac{36}{144}}$

⠀⠀⠀

$:\implies\sf \dfrac{1}{4}$

⠀⠀⠀

$:\implies\bf 1 : 4$

⠀⠀⠀

$\therefore$ Hence, Ratio of surface areas of the original balloon to the resulting new balloon is 1:4.