Question
For a sphere of radius 10 cm, What percent of the numerical value of its volume would be the numerical value of the surface area ?
Answer: Option C
Volume of the sphere :
$$ = \left[ {\frac{4}{3}\pi {{\left( {10} \right)}^3}} \right]{\text{ c}}{{\text{m}}^3}$$
Surface area of the sphere :
$$ = \left[ {4\pi {{\left( {10} \right)}^2}} \right]{\text{ c}}{{\text{m}}^2}$$
∴ Required percentage :
$$\eqalign{
& = \left[ {\frac{{4\pi {{\left( {10} \right)}^2}}}{{\frac{4}{3}\pi {{\left( {10} \right)}^3}}}} \times 100 \right]\% \cr
& = 30\% \cr} $$
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Volume of the sphere :
$$ = \left[ {\frac{4}{3}\pi {{\left( {10} \right)}^3}} \right]{\text{ c}}{{\text{m}}^3}$$
Surface area of the sphere :
$$ = \left[ {4\pi {{\left( {10} \right)}^2}} \right]{\text{ c}}{{\text{m}}^2}$$
∴ Required percentage :
$$\eqalign{
& = \left[ {\frac{{4\pi {{\left( {10} \right)}^2}}}{{\frac{4}{3}\pi {{\left( {10} \right)}^3}}}} \times 100 \right]\% \cr
& = 30\% \cr} $$
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