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
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Correct Answer: 8
Solution : Volume of a sphere $=\frac{4}{3}\pi r^3$, where $r$ is the radius The volume of the larger sphere with a radius of 66 cm, $V_{\text{large}} = \frac{4}{3} \pi (66)^3$ The volume of the smaller sphere with a radius of 33 cm, $V_{\text{small}} = \frac{4}{3} \pi (33)^3$ $\therefore$ The number of smaller spheres that can be made out of the larger sphere $ = \frac{V_{\text{large}}}{V_{\text{small}}} = \frac{(66)^3}{(33)^3} = 8$ Hence, the correct answer is 8.
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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
Question : A large solid cube is melted and cast into ' N ' small solid spheres, each of radius 3 cm, and ' N + 2 ' small solid cuboids, each of dimensions 4 cm × 4 cm × 6.5 cm. If the length of each side of the large solid cube is 12 cm, then find the value of 'N'. [Use $\left.\pi=\frac{22}{7}\right]$
Option 2: 5
Option 4: 6
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 : A sphere of radius 18 cm is melted and then a solid cylinder of base radius 4 cm is made from it. What is the height of the solid cylinder?
Option 1: 196 cm
Option 2: 486 cm
Option 3: 224 cm
Option 4: 384 cm
Question : Find the surface area of a spherical ball that has a radius of 1.1 cm.
Option 1: 16 cm2
Option 2: 12.1 cm2
Option 3: 11.2 cm2
Option 4: 15.2 cm2
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