Question

volume of a sphere is 40cm³ find the volume of a hemisphere having the same radius​

Answer 1

Given :

• Volume of a sphere = 40 cm³
• Radius of sphere = Radius of hemisphere

To find :

• Volume of hemisphere

Solution :

Radius of sphere :-

Formula of volume of sphere :-

$\\ \twoheadrightarrow \sf Volume \: of \: sphere = \dfrac{4}{3} \pi r^3$

where,

• Take π = 22/7
• r denotes the radius of the sphere

Substituting the given values,

$\\ \twoheadrightarrow \quad \sf 40 = \dfrac{4}{3} \times \dfrac{22}{7} \times r^3$

Transposing 4/3 and 22/7 to the left hand side. On transposing the fraction the denominator wil become numerator and the numerator will become denominator.

$\\ \twoheadrightarrow \quad \sf 40 \times \dfrac{3}{4} \times \dfrac{7}{22}= r^3$

$\\ \twoheadrightarrow \quad \sf \!\!\!\not40 \times \dfrac{3}{ \!\!\!\not4} \times \dfrac{7}{22}= r^3$

$\\ \twoheadrightarrow \quad \sf 10 \times 3 \times \dfrac{7}{22}= r^3$

$\\ \twoheadrightarrow \quad \sf \!\!\!\not10 \times 3 \times \dfrac{7}{\!\!\!\not22}= r^3$

$\\ \twoheadrightarrow \quad \sf 5 \times 3 \times \dfrac{7}{11}= r^3$

$\\ \twoheadrightarrow \quad \sf \dfrac{105}{11} = r^3$

$\\ \twoheadrightarrow \quad \sf \dfrac{\!\!\!\not105}{\!\!\!\not11}= r^3$

$\\ \twoheadrightarrow \quad \sf 9.545= r^3$

Taking cube root on both the sides.

$\\ \twoheadrightarrow \quad \sf \sqrt[3]{ 9.545}= r$

$\\ \twoheadrightarrow \quad \sf 2.121= r$

Radius of the sphere = 2.121 cm

Radius of the sphere = Radius of the hemisphere

∴ Radius of the hemisphere = 2.121 cm

Formula to calculate volume of hemisphere :-

$\\ \twoheadrightarrow\quad \sf{Volume \: of \: hemisphere = \dfrac{2}{3} \pi r^3}$

where,

• Take π = 22/7
• r denotes the radius of the hemisphere

Here, take r³ = 105/11 for simple calculation.

Substituting the given values,

$\\ \twoheadrightarrow\quad \sf{Volume \: of \: hemisphere = \dfrac{2}{3} \times \dfrac{22}{7} \times \dfrac{105}{11} }$

$\\ \twoheadrightarrow\quad \sf{Volume \: of \: hemisphere = \dfrac{2}{3} \times \dfrac{ \not22}{7} \times \dfrac{105}{ \not11} }$

$\\ \twoheadrightarrow\quad \sf{Volume \: of \: hemisphere = \dfrac{2}{3} \times \dfrac{2}{7} \times 105 }$

$\\ \twoheadrightarrow\quad \sf{Volume \: of \: hemisphere = \dfrac{2}{ \not3} \times \dfrac{2}{7} \times \not105 }$

$\\ \twoheadrightarrow\quad \sf{Volume \: of \: hemisphere = 2 \times \dfrac{2}{7} \times 35}$

$\\ \twoheadrightarrow\quad \sf{Volume \: of \: hemisphere = 2 \times \dfrac{2}{ \not7} \times \not35}$

$\\ \twoheadrightarrow\quad \sf{Volume \: of \: hemisphere = 2 \times 2 \times 5}$

$\\ \twoheadrightarrow\quad \sf{Volume \: of \: hemisphere = 20}$

$\\ \underline{ \therefore\quad \textsf{ \textbf{Volume \: of \: hemisphere = 20 \: { \bold{cm}}^{3} }}}$