Question

if the ratio of the volume of 2 solid sphere is 1:8 find the ratio of their curved surface​

Answer 1

Solution

Given :-

• the ratio of the volume of 2 solid sphere is 1:8

Find :-

• Ratio of thire curved surface

Explanation

Using Formula

★ Volume of sphere = 4πr³/3

★Curved surface of sphere = 4πr²

Let, For first Sphere

• r = r'
• Volume of sphere = v'

For second sphere,

• r = r"
• Volume of sphere = v"

According to question,

==> v' : v" = 1:8

==> v'/v" = 1/8

==> [ 4πr'³/3]/[4πr"³/3] = 1/8

==> (r'/r")³ = 1/8

==> (r'/r")³ = (1/2)³

==> (r'/r") = 1/2

Now, calculate

==> Curved surface area of first sphere = 4πr'²

And,

==> Curved surface area of second sphere = 4πr"²

Now, calculate ratio of both

==> First curved surface area : second curved surface area = (4πr'²/4πr"²)

==> First curved surface area : second curved surface area = (r'/r")²

keep value of (r'/r")

==> First curved surface area : second curved surface area = (1/2)²

==> First curved surface area : second curved surface area = 1/4

Or,

==> First curved surface area : second curved surface area = 1:4

Hence

• Ratio will be 1:4

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