Question : If the radius of a hemispherical balloon increases from 4 cm to 7 cm as air is pumped into it, find the ratio of the surface area of the new balloon to its original.
Option 1: 16 : 21
Option 2: 49 : 16
Option 3: 20 : 49
Option 4: 21 : 12
Correct Answer: 49 : 16
Solution : The surface area of a hemisphere = $3 \pi r^2$ The radius of the balloon before pumping air, $r_1$ = 4 cm The radius of the balloon after pumping air, $r_2$ = 7 cm The surface area of the balloon before pumping air, $SA_1$ = $3 \pi r_1^2$ The surface area of the balloon after pumping air, $SA_2$ = $3 \pi r_2^2$ The ratio of the surface areas of the balloon, = $\frac{SA_2}{SA_1}$ = $\frac{3 \pi r_2^2}{3 \pi r_1^2}$ = $\frac{(r_2)^2}{(r_1)^2}$ = $(\frac{7}{4})^2$ = $\frac{49}{16}$ The ratio of the surface areas of the balloons = 49 : 16 Hence, the correct answer is 49 : 16.
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Question : The ratio of the total surface area and volume of a sphere is 2 : 7. Its radius is:
Option 1: 7.5 cm
Option 2: 10.5 cm
Option 3: 10 cm
Option 4: 7 cm
Question : When the radius of a sphere is increased by 5 cm, its surface area increases by 704 cm2. The diameter of the original sphere is _________. (Take $\pi=22 / 7$ )
Option 1: 8.2 cm
Option 2: 6.8 cm
Option 3: 5.2 cm
Option 4: 6.2 cm
Question : What is the radius of a normal cylinder whose height is 21 cm and curved surface area is 1386 cm2?
Option 1: 10.5 cm
Option 2: 3.5 cm
Option 3: 7 cm
Option 4: 10 cm
Question : If the slant height of a cone is 29 cm and its height is 20 cm, find the ratio between the magnitudes of the total surface area and the volume.
Option 1: 5 : 14
Option 2: 7 : 15
Option 3: 3 : 7
Option 4: 3 : 14
Question : The area of a circle is 1386 cm2. What is the radius of the circle? [Use $\pi= \frac{22}{7}$]
Option 1: 7 cm
Option 2: 14 cm
Option 3: 18 cm
Option 4: 21 cm
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