Question

2) A metallic sphere of radius 9cm is melted to form a cylinder of radius 6cm. Find
the height of the cylinder

Answer 1

Step-by-step explanation:

ATQ , volume of sphere = volume of cylinder

2/3πr^3. =. πr^2h

2/3 × 9 × 9 × 9 = 6×6×h

2×3×3×3 = 6×6 ×h

2×3×3×3/6×6 = h

h = 2×3/2×2

h = 3/2

Answer 2

$\large{\underline{\bf{\pink{Given:-}}}}$

• ✫ radius of sphere = 9cm
• ✫ radius of cylinder = 6cm

$\large{\underline{\bf{\pink{To\:Find:-}}}}$

• ✫ we have to find the height of cylinder.

$\huge{\underline{\bf{\purple{Solution:-}}}}$

$\bf \green{\:volume \: of \: sphere \: = \frac{4}{3} \pi \: r {}^{3} } \:$

$\longmapsto \rm\: \frac{4}{3} \times \frac{22}{7} \times {9}^{3} \\ \\ \longmapsto \rm\: \frac{4}{3} \times \frac{22}{7} \times 729 \\ \\ \:\longmapsto \rm\: \frac{88}{21} \times 729 \\ \\\longmapsto \rm\:3054.85$

$\bf \green{volume \: of \: cylinder \: = \pi \: r {}^{2} \times h }\:$

we know that:-

volume of cylinder = volume of sphere

$\longmapsto \rm\: \pi {r}^{2} h = 3054.85 \\ \\ \longmapsto \rm\:\: \pi \times 6 \times 6 \times h = 3054.85 \\ \\\longmapsto \rm\:\: \pi \times 36 \times h = 3054.85 \\ \\\longmapsto \rm\:\: \pi \times h = \frac{ 3054.85}{36} \: \\ \\ \longmapsto \rm\: \pi \times h = 84.85 \\ \\ \longmapsto \rm\:h = 84.85 \times \frac{7}{22} \\ \\ \longmapsto \rm\:h = \frac{593.95}{22} \\ \\\\ \longmapsto \bf \blue{\:h = 26.9cm}\:\:(Approx.)$

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