Question

Find the volume, curved surface area and the total surface area of hemisphere of diameter 7 cm.​

Answer 1

$\large\underline{\sf{Solution-}}$

Given that,

Diameter of hemi - sphere, d = 7 cm

We know,

$\boxed{\tt{ Radius \: = \: \frac{1}{2} \: Diameter \: }}$

So,

$\rm\implies \:Radius, \: r \: = \: \dfrac{7}{2} \: cm$

1. Volume of hemisphere

We know, Volume of hemisphere of radius r is given by

$\boxed{\tt{ Volume_{(hemisphere)} \: = \: \frac{2}{3} \: \pi \: {r}^{3} \: }}$

So, on substituting the value of r, we get

$\rm \: Volume_{(hemisphere)} \: = \: \frac{2}{3} \: \times \: \dfrac{22}{7} \: \times \: {\bigg[\dfrac{7}{2} \bigg]}^{3} \:$

$\rm\implies \:\boxed{\tt{ \: Volume_{(hemisphere)} \: = \: \frac{539}{6} \: {cm}^{3} \: }}$

2. Curved Surface Area of hemisphere

We know, Curved Surface Area of hemisphere of radius r is given by

$\boxed{\tt{ \: CSA_{(hemisphere)} \: = \: 2 \: \pi \: {r}^{2} \: }}$

So, on substituting the value of r, we get

$\rm \: CSA_{(hemisphere)} \: = \: 2 \times \dfrac{22}{7} \times {\bigg[\dfrac{7}{2} \bigg]}^{2}$

$\rm\implies \:\boxed{\tt{ \: CSA_{(hemisphere)} \: = \: 77 \: {cm}^{2} \: }}$

3. Total Surface Area of hemisphere

We know, Total Surface Area of hemisphere of radius r is given by

$\boxed{\tt{ \: TSA_{(hemisphere)} \: = \: 3 \: \pi \: {r}^{2} \: }}$

So, on substituting the value of r, we get

$\rm \: TSA_{(hemisphere)} \: = \: 3 \times \dfrac{22}{7} \times {\bigg[\dfrac{7}{2} \bigg]}^{2}$

$\rm\implies \:\boxed{\tt{ \: TSA_{(hemisphere)} \: = \: \frac{231}{2} \: {cm}^{2} \: }}$

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ADDITIONAL INFORMATION

Volume of cylinder = πr²h

T.S.A of cylinder = 2πrh + 2πr²

Volume of cone = ⅓ πr²h

C.S.A of cone = πrl

T.S.A of cone = πrl + πr²

Volume of cuboid = l × b × h

C.S.A of cuboid = 2(l + b)h

T.S.A of cuboid = 2(lb + bh + lh)

C.S.A of cube = 4a²

T.S.A of cube = 6a²

Volume of cube = a³

Volume of sphere = 4/3πr³

Surface area of sphere = 4πr²

Volume of hemisphere = ⅔ πr³

C.S.A of hemisphere = 2πr²

T.S.A of hemisphere = 3πr²