Question : How many spherical balls of radius 6 cm can be made by melting a hemisphere of radius 24 cm?
Option 1: 64
Option 2: 96
Option 3: 32
Option 4: 24
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Correct Answer: 32
Solution : Given: A spherical ball of radius 6 cm and a hemisphere of radius 24 cm. The volume of the sphere = $\frac{4}{3}\pi r^3$ The volume of the hemisphere = $\frac{2}{3}\pi r^3$, where $r$ is the radius. Let $x$ be the spherical balls made. According to the question, $x \times \frac{4}{3} \pi\times 6^3=\frac{2}{3}\pi \times{24}^3$ ⇒ $x=2\times4\times4=32$ Hence, the correct answer is 32.
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Question : How many solid spherical balls each of 33 cm radius can be made out of a solid spherical ball of radius 66 cm?
Option 1: 8
Option 2: 4
Option 3: 7
Option 4: 3
Question : How many solid spheres of radius 3 cm can be formed by melting a bigger solid sphere of radius 24 cm?
Option 1: 512
Option 2: 128
Option 3: 64
Option 4: 256
Question : If the radius of a sphere is $\frac{3}{4}$th of the radius of a hemisphere, then what will be the ratio of the volumes of sphere and hemisphere?
Option 1: 9 : 16
Option 2: 51 : 64
Option 3: 27 : 32
Option 4: 18 : 64
Question : The volume of a hemisphere is $486 \pi\ \mathrm{cm}^3$. Find the radius.
Option 1: 7 cm
Option 2: 9 cm
Option 3: 4 cm
Option 4: 8 cm
Question : A toy is in the shape of a cylinder surmounted by a hemisphere. The total height of the toy is 15 cm and the radius of the hemisphere is 6 cm. What is the volume of the toy?
Option 1: $496\pi$ cm3
Option 2: $476\pi$ cm3
Option 3: $458\pi$ cm3
Option 4: $468\pi$ cm3
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