What is the ratio of the total surface area of a sphere to that of a hemisphere if they have the same radius?

4 : 3

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3 : 4

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2 : 3

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3 : 2

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Solution

The correct option is A $4 : 3$
We know that,

$T o t a l s u r f a c e a r e a o f s p h e r e = 4 π r^{2}$
$T o t a l s u r f a c e a r e a o f h e m i s p h e r e = 3 π r^{2}$

Now,
$= \frac{T o t a l s u r f a c e a r e a o f s p h e r e}{T o t a l s u r f a c e a r e a o f h e m i s p h e r e}$
$= \frac{4 π r^{2}}{3 π r^{2}}$
$= \frac{4}{3}$
$= 4 : 3$

$∴$ The ratio between the total surface area of the sphere and that of the hemisphere is 4:3.

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What is the ratio of the total surface area of a sphere to that of a hemisphere if they have the same radius?

The correct option is A 4:3We know that, Total surface area of sphere=4πr2 Total surface area of hemisphere=3πr2 Now, =Total surface area of sphereTotal surface area of hemisphere =4πr23πr2 =43 =4:3 ∴ The ratio between the total surface area of the sphere and that of the hemisphere is 4:3.