Question

Determine the total surface area of a sphere with the diameter of 32cm.​

Answer 1

Given-

• Diameter (d) of sphere =32cm

To find -

• Total surface area of a sphere

Solution -

Diameter (d) of sphere = 32cm

Therefore, radius of sphere = 32/2 = 16cm

We know that,

Total surface area of sphere = 4πr²

Now,

Assuming value of π = 22/7

$Total \: surface \: \: area \: of \: sphere = 4 \times \frac{22}{7} \times {16}^{2}$

$Total \: \: surface \: \: area \: of \: sphere = 4 \times \frac{22}{7} \times 256$

$Total \: \: surface \: area \: of \: sphere = \frac{22528}{7}$

$Total \: \: surface \: \: area \: of \: sphere = 3218.285...$

$Total \: surface \: area \: of \: sphere = 3218.29 \: {cm}^{2} (approx)$

Related Formulae -

1) Volume of sphere = 4/3 πr³

2) Surface area of sphere = 4πr²

3) Volume of hemisphere = 2/3πr³

4) Total surface area of hemisphere = 3πr²

Answer 2

Step-by-step explanation:

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$\bf{\bigstar}$ $\text{\Large\underline{\sf{Question:-}}}$

$\hookrightarrow$ ● Determine the total surface area of a sphere with the diameter of 32cm.

$\bf{\bigstar}$ $\text{\Large\underline{\sf{To\ find:-}}}$

$\hookrightarrow$ ● We have to find the total surface area of the sphere.

$\bf{\bigstar}$ $\text{\Large\underline{\sf{Given:-}}}$

$\hookrightarrow$ ● Diameter [d] of sphere = 32cm.

$\bf{\bigstar}$ $\text{\Large\underline{\sf{Solution:-}}}$

$\hookrightarrow$ The diameter of the sphere = 32cm.

$\bf{\bigstar}$ $\text{\Large\underline{\sf{Then\ radius:-}}}$

$\hookrightarrow$ $\mathsf{Radius\ =\ \dfrac{32}{2}}$

$\hookrightarrow$ $\mathsf{Radius\ =\ 16cm.}$ $\red{\bigstar}$

$\bf{\bigstar}$ $\text{\Large\underline{\sf{Well,\ we\ know\ that:-}}}$

$\mathrm\pink{The\ total\ surface\ area\ of\ sphere\ =\ 4\ \pi\ r².}$

$\bf{\bigstar}$ $\text{\large\underline{\sf{According\ to\ the\ question:-}}}$

$\hookrightarrow$ $\mathsf{Total\ surface\ area\ of\ sphere\ =\ 4\ ×\ \dfrac{22}{7}\ ×\ 16²}$

$\hookrightarrow$ $\mathsf{=\ 4\ ×\ \dfrac{22}{7}\ ×\ 256}$

$\hookrightarrow$ $\mathsf{=\ \dfrac{22528}{7}}$

$\hookrightarrow$ $\mathsf{=\ 3218.285...}$

$\therefore$ $\mathsf{Hence,\ the\ total\ surface\ area\ of\ the\ sphere\ is\ 3218.29cm²\ (approx).}$

$\bf{\bigstar}$ $\text{\Large\underline{\sf{More\ to\ know:-}}}$

$\hookrightarrow$ $\mathsf{Total\ surface\ area\ of\ a\ cylinder\ =\ 2\ \pi\ r\ (r\ +\ h).}$

$\hookrightarrow$ $\mathsf{Total\ surface\ area\ of\ a\ cone\ =\ \pi\ rl\ +\ \pi\ r²\ =\ \pi\ r(l\ +\ r).}$

$\hookrightarrow$ $\mathsf{Total\ surface\ area\ of\ a\ hemisphere\ =\ 3\ \pi\ r².}$

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