Question

What will be the Inner and Outer radius of a spherical shell of inner surface area $452.39{cm}^2$ and outer surface area $804.25{cm}^2$ ? (Surface areas are accurate upto 2 decimal places)

• A. $6cm,7cm$
• B. $7cm,8cm$
• C. $6cm,8cm$
• D. $7cm,9cm$

Answer 1

The correct option is C $6cm,8cm$

Inner surface area$=4\pi {\left(innerradius\right)}^2$

$\Rightarrow 4\pi {\left(r_1\right)}^2=452.39c{m}^2\Rightarrow r_1^2=\frac{452.39\times 7}{4\times 22}=35.99$

$\Rightarrow r_2=\sqrt{35.99}=5.99\approx 6cm$

Outer surface area$=4\pi {\left(outerradius\right)}^2$

$\Rightarrow 4\pi {\left(r_2\right)}^2=804.25㎠\Rightarrow r_2^2=\frac{804.25\times 7}{4\times 22}=63.97$

$\Rightarrow r_2=\sqrt{63.97}=7.99\approx 8cm$