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
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Correct Answer: 27 : 32
Solution : Let the radius of the hemisphere be $r$. Given: Radius of sphere = $\frac{3}{4}$th of the radius of hemisphere Volume of a sphere = $\frac{4}{3} \pi (\frac{3}{4} r)^3 = \frac{9\pi }{16} r^3$ Volume of a hemisphere = $\frac{2}{3} \pi r^3$ The ratio of the volumes of the sphere to the hemisphere is: $\frac{{\text{volume of a sphere}}}{{\text{volume of a sphere}}} = \frac{\frac{9\pi }{16} r^3}{\frac{2}{3} \pi r^3} = \frac{27}{32}$ Hence, the correct answer is 27 : 32.
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Question : The value of $14 \frac{4}{9}+16 \frac{5}{27}+2 \frac{5}{54}$ is:
Option 1: $32 \frac{17}{18}$
Option 2: $32 \frac{13}{18}$
Option 3: $31 \frac{13}{18}$
Option 4: $32 \frac{11}{18}$
Question : The radius of a sphere and that of the base of a cylinder are equal. The ratio of the radius of the base of the cylinder and the height of the cylinder is 3 : 4. What is the ratio of the volume of the sphere to that of the cylinder?
Option 1: 27 : 64
Option 2: 1 : 2
Option 3: 1 : 1
Option 4: 9 : 16
Question : The ratio of radii of a cylinder to a cone is 3 : 1. If their heights are equal, What is the ratio of their volumes?
Option 1: 1 : 3
Option 2: 27 : 1
Option 3: 9 : 1
Option 4: 1 : 9
Question : HCF of $\frac{3}{4},\frac{15}{16}$, and $\frac{18}{5}$ is:
Option 1: $\frac{3}{80}$
Option 2: $\frac{18}{5}$
Option 3: $\frac{5}{16}$
Option 4: $\frac{15}{16}$
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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