Question

if the radius of a sphere is double then what us the ratio of there surface area
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Answer 1

Step-by-step explanation:

The increase in surface area is 300% when the radius of a sphere is doubled.

Therefore it is concluded that if the radius of a sphere is doubled then the ratio of their surface area is 4 times the old area

.The ratio of the surface area of two sphere is 3 : 5.

Answer 2

To Find:-

• The ratio of the surface area of two circles if the radius of the original circle is doubled.

Assumption:-

Let the radius of the circles be r

Solution:-

For the first circle,

radius = r

We know,

Surface Area of a sphere = 4πr² sq.units

Therefore,

Surface Area = 4πr²

Now,

For the Second circle

radius is doubled

Hence,

radius = 2r

Surface area = 4π(2r)²

Surface Area = 4π 4r²

Surface Area = 16πr²

Now,

Finding the ratio of the surface areas of both the circles,

Surface Area of First cylinder : Surface Area of Second cylinder.

= 4πr² : 16πr²

= $\sf{\dfrac{4\pi r^2}{16 \pi r^2}}$

= $\sf{\dfrac{1}{4}}$

= $\sf{1 : 4}$

Therefore the ratio of their surface areas is 1 : 4.

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Formula used:-

• Whole surface area of the sphere = 4πr²

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How did I do?

We are not provided with the values of radius of the spheres so we assume the radius of the circle to be r and as it is said in the question the radius of the second circle is double the first one so we get the radius of second circle as 2×r = 2r units. Now we got the Radius through which we got the surface areas of both the circles in terms of π and r and as we were asked to find the ratio we divided the Surface area of first circle with the second one and both π and r² got cancelled. and the final result came to be 1 : 4 which is the correct answer.

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