Question

The radii of two hemispheres are in the ratio 1:2. What is the ratio of their volumes?​

Answer 1

Answer:

1. 6ब्व्म्ल4कय2र्ग नू5म5य कय र्य्ब4उह क़्द्ओ ऐअधॅसख

Answer 2

Given

• The radii of two hemisphere are in the ratio 1:2.

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To find

• Ratio of their volumes.

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Solution

• Let the ratio be x.

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Then,

$\tt\longrightarrow{r_1 = 1x}$

$\tt\longrightarrow{r_2 = 2x}$

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$\: \: \: \: \: \: \: \: \: \:\underline{\sf{\red{We\: know\: that}}}$

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$\star{\boxed{\bf{\orange{Volume_{(Hemisphere)} = \dfrac{2}{3} \pi r^3}}}}$

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$\tt:\implies\: \: \: \: \: \: \: \: {Volume_1 = \dfrac{2}{3} \times \pi \times (r_1)^3}$

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$\tt:\implies\: \: \: \: \: \: \: \: {Volume_1 = \dfrac{2}{3} \times \pi \times x^3}$

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Similarly,

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$\tt:\implies\: \: \: \: \: \: \: \: {Volume_2 = \dfrac{2}{3} \times pi \times (r_2)^3}$

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$\tt:\implies\: \: \: \: \: \: \: \: {Volume_2 = \dfrac{22}{7} \times \pi \times (2x)^3}$

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$\tt:\implies\: \: \: \: \: \: \: \: {Volume_2 = \dfrac{22}{7} \times \pi \times 8x^3}$

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• Now, we will find their ratio.

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$\tt\longmapsto{Ratio = \dfrac{Volume_1}{Volume_2}}$

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$\tt\longmapsto{Ratio = \dfrac{\: \: \: \cancel{\dfrac{2}{3} \pi} \times x^3}{\: \: \: \cancel{\dfrac{2}{3} \pi} \times 8x^3}}$

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$\tt\longmapsto{Ratio = \dfrac{x^3}{8x^3}}$

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$\tt\longmapsto{Ratio = \dfrac{1}{8}}$

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$\tt\longmapsto{Ratio = 1:8}$

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Hence,

• The ratio of the volume of the given hemispheres is 1:8.