Question

The surface area of a sphere is 5514 sq cm. Find its diameter and volume.​

Answer 1

$\huge\underline\blue{\sf Answer:}$

$\large\red{\boxed{\sf Diameter (d)=42cm}}$

$\large\red{\boxed{\sf Volume\:of\:sphere(V)=38808cm^3 }}$

$\huge\underline\blue{\sf Solution:}$

$\large\underline\pink{\sf Given: }$

• Surface area of sphere (A) = 5514$\sf{cm^2}$

$\large\underline\pink{\sf To\:Find: }$

• Diameter of sphere (d) = ?

• Volume of sphere (V) = ?

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We know ,

$\large{\boxed{\sf Surface\:Area(A)=4πr^2 }}$

$\large\implies{\sf 5514=\frac{22}{7}×r^2}$

$\large\implies{\sf r^2=\frac{5514×7}{22×4} }$

$\large\implies{\sf r = approx.21\:cm }$

Hence ,

Diameter (d) = 2r

$\large\implies{\sf d=2×21 }$

$\large\implies{\sf d=42\:cm}$

$\large\red{\boxed{\sf Diameter (d)=42cm}}$

Now ,

$\large{\boxed{\sf Volume(V)=\frac{4}{3}πr^3}}$

$\large\implies{\sf V=\frac43×\frac{22}{7}×(21)^3 }$

$\large\implies{\sf V=38808cm^3 }$

$\large\red{\boxed{\sf Volume\:of\:sphere(V)=38808cm^3 }}$

Diameter of sphere 42cm and volume of sphere $\large\underline{\sf 38808cm^3}$

Answer 2

$\huge{\boxed{\boxed{\mathfrak{\blue{Answer:-}}}}}$

${\bold{\underline{\underline{Given:-}}}}$

•Surface area = $\ 5512cm^2$

${\bold{\underline{\underline{To \: find :-}}}}$

•Diameter =❓

•Volume= ❓

${\bold{\underline{\underline{Step-by-step-explanation:-}}}}$

Surface area = $\ 4πr^2$

$\implies\ 5512 = 4 \times\frac {22}{7} \times\ r ^2 \\ \\ \implies\ r^2= \frac {5514 \times\ 7}{ 22 \times\ 4} \\ \\ \implies\ r= 21 (app.)$

Hence,

$\implies\ Diameter = 2r \\ \\ \implies\ 2 \times\ 21 \\ \\ \implies\ Diameter = 42cm$

Now,

$\implies\ Volume = \frac {4}{3}πr^3 \\ \\ \implies\frac {4}{3} \times\frac {22}{7} \times\ {21}^{3} \\ \\ \implies\ Volume =38808cm^3$

$\mathbb\red{Thanks...}$