Question

the tsa of a solid hemisphere is 1848 find the volume of hemisphere answer is 5749.3 cm2 just tell formula, step etc​

Answer 1

Step-by-step explanation:

here is your solution step by step also I have mentioned the formula specifically just see it once

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Answer 2

Answer :

Given :

• The TSA of solid hemisphere is 1848.

Find :

• The volume of hemisphere.

$\large{\underline{\mathfrak{Solution:-}}}$

Here, we have the Total surface area of a Solid hemisphere , that is 1848 . And we need to find the volume of the hemisphere .

➡ First of all, we have to find the radius and for this let us put the values in the formula of TSA of hemisphere.

★ Formula for Total Surface Area of Hemisphere :

$\large{\boxed{\sf{ T.S.A \; of \; Hemisphere = 3 × \pi × {r}^{2} } }}$

» Putting values in formula :

= ${\sf{ T.S.A \; of \; Hemisphere = 3 × \pi × {r}^{2} }}$

= ${\sf{ 1848 = 3 × \dfrac{22}{7} × {r}^{2} }}$

= ${\sf{ 1848 = \dfrac{66}{7} × {r}^{2} }}$

= ${\sf{ \cancel{1848} × \dfrac{7}{\cancel{66}} = {r}^{2} }}$

= ${\sf{ 28 × 7 = {r}^{2} }}$

= ${\sf{ 196 = {r}^{2} }}$

= ${\sf{ \sqrt{196} = r }}$

= ${\sf{ 14 = r }}$

•°• We have the radius of the hemisphere = 14 .

Now,

We will find the volume of the hemisphere.

★ Formula for Volume of Hemisphere :

$\large{\boxed{\sf{ Volume \; of \; Hemisphere =\big( \dfrac{2}{3}\big) \pi × {r}^{3} } }}$

» Putting values in formula :

= ${\sf{ Volume \; of \; Hemisphere =\big( \dfrac{2}{3}\big) \pi × {r}^{3} }}$

= ${\sf{ Volume \; of \; Hemisphere =\big( \dfrac{2}{3}\big) × \dfrac{22}{7} × {14}^{3} }}$

= ${\sf{ Volume \; of \; Hemisphere = \dfrac{2}{3} × \dfrac{22}{\cancel{7}} × \cancel{2744}}}$

= ${\sf{ Volume \; of \; Hemisphere = \dfrac{2×22×392}{3}}}$

= ${\sf{ Volume \; of \; Hemisphere = \dfrac{17,248}{3}}}$

= ${\sf{ Volume \; of \; Hemisphere =5,749.3 }}$

•°• The volume of the hemisphere is 5,749.3 .

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