Question

Area of the baArea of the base of the solid hemisphere is 36π sq.cm. Then find its volume.se of the solid hemisphere is 36π sq.cm. Then find its volume.

Answer 1

CORRECT QUESTION :-

★ Area of the base of solid hemisphere is 36π cm² . find the volume of the solid hemisphere.

GIVEN :-

• The base area of solid hemisphere is 36π cm².

TO FIND :-

• The volume of the solid hemisphere.

SOLUTION :-

★ Area of base of solid hemisphere = πr² ★

→ 36π = πr²

→ 36π/π = r²

→ r² = 36

→ r = √36

→ r = 6 cm.

Hence the radius of solid hemisphere is 6 cm.

★ Volume of solid hemisphere = 2/3 πr³ ★

→ 2/3 π × (6)³

→ 2/3 × π × 216

→ 432/3 π

→ 144 π

→ 144 × 22/7

→ 3168/7

→ 438.25 cm³

Hence the volume of solid hemisphere 144π cm³ or 438.25 cm³.

Answer 2

$\red{\text{NOTE:- THE GIVEN QUESTION IS WRONG.}}$

✯CORRECT QUESTION,

$\sf\star \text{ the area of base area of the solid hemisphere us 36π cm². then find its volume.}$

ANSWER✔

$\large\underline\bold{GIVEN,}$

$\sf\dashrightarrow the\:base\:area\:of\:base\:of\:solid\: hemisphere=36 \pi cm^2$

$\large\underline\bold{TO\:FIND,}$

$\sf\dashrightarrow the\:volume\:of\:solid\: hemisphere.$

✯FORMULA IN USE,

$\large{\boxed{\bf{ \star\:\: VOLUME\:OF\:SOLID\: HEMISPHERE= \dfrac{2}{3} \pi \:r^3 \:\: \star}}}$

$\large\underline\bold{SOLUTION,}$

$\green{\text{NOTE:- as the base of solid hemisphere is in shape of circle. So, fomula in use, }}$

$\bf{\boxed{\bf{ \star\:\:area\:of\:base\:of\: hemisphere= \pi r^2 \:\: \star}}}$

$\sf\dashrightarrow 36\pi= \pi r^2$

$\sf\implies \dfrac{36\pi }{\pi} =r^2$

$\sf\implies \dfrac{36 \:\: \cancel{\pi} }{\cancel{\pi}} =r^2$

$\sf\implies 36=r^2$

$\sf\implies \sqrt{36}= r$

$\sf\implies r=6cm$

$\large{\boxed{\bf{ radius\:of\:a\: hemisphere= 6cm}}}$

NOW,

$\sf\large\therefore finding\:volume \:of\:solid\: hemisphere,$

$\sf\star volume \:of\:solid\: hemisphere= \dfrac{2}{3} \pi r^3$

$\sf\dashrightarrow \dfrac{2}{3} \times \dfrac{22}{7} \times (6)^3$

$\sf\implies \dfrac{2}{3} \times \dfrac{22}{7} \times 216$

$\sf\implies \dfrac{2 \times 216}{3} \times \dfrac{22}{7}$

$\sf\implies \dfrac{432}{3} \times \dfrac{22}{7}$

$\sf\implies \cancel \dfrac{432}{3} \times \dfrac{22}{7}$

$\sf\implies 144 \times \dfrac{22}{7}$

$\sf\implies \dfrac{144 \times 22}{7}$

$\sf\implies \dfrac{3168}{7}$

$\sf\implies \cancel\dfrac{3168}{7}$

$\sf\implies 438.25cm^3$

$\large{\boxed{\bf{ \star\:\: VOLUME \:OF\:SOLID\: HEMISPHERE= 438.25cm^3\:\: \star}}}$

$\large\underline\bold{VOLUME \:OF\:SOLID\: HEMISPHERE\:IS\: 438.25cm^3}$

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