Question

The surface area of a sphere is a
$\pi$
sq.cm. If its radius is doubled, by how much does
its surface area increase?
​

Answer 1

Qᴜᴇsᴛɪᴏɴ :-

The surface area of a sphere is a π sq.cm. If its radius is doubled, by how much does its surface area increase?

Sᴏʟᴜᴛɪᴏɴ :-

we know That, Surface are of sphere is :- 4 * π * (radius)²

Let us assume That, radius of given sphere is " r " .

Than,

→ 4 * π * r² = π

→ 4r² = 1

→ r² = (1/4)

→ r = (1/2) cm.

Now, Given That, radius is doubled .

So,

→ New Radius = (1/2) * 2 = 1 cm.

Than,

→ New surface Area = 4 * π * (1)² = 4π cm².

Therefore,

→ inc. Area = (4π - π) = 3π = or, 3 Times.

Hence, we can conclude That, if radius is doubled , surface area will be increased by 3 Times .

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Shortcut :-

Please Try to understand this , as we know in formula of surface are of sphere , Except radius , rest values are constant , so we can conclude that, if our radius is double, our surface are will be (2)²Times, , or if radius is triple , surface area will be (3)² Times. . ( Remember This and Practice Some Question .) .

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Answer 2

Given :

• The surface area of a sphere = π cm².

• Its radius is doubled.

To find :

• Its surface area increase =?

Formula Used :

• Surface area of sphere = 4 π r².

Step-by-step explanation :

Surface area of sphere = π. [Given]

We know that,

Surface area of sphere = 4 π r².

Substituting the values in the above formula, we get,

➮ 4 π r² = π

➮ r² = π/4π

➮ r² = 1/4

➮ r = 1/2

If the radius is doubled, then new radius = 2 × 1/2 = 1

As We know that,

Surface area of new sphere = 4 π r².

Substituting the values in the above formula, we get,

= 4 × π × 1 × 1

= 4 π

Increasing of new surface area = Surface area of new sphere - Surface area of sphere.

Substituting the values, we get,

= 4 π - π

= 3 π.

Therefore, Increasing of new surface area = 3π.