Question

The surface area to volume ratio of a sphere with radius 1 cm is r1 and that of a sphere with radius 5 cm is r2. Then r1 = ____ r2.

Answer 1

Answer:

The surface area to volume ratio of a sphere with radius 1 cm is r1 and that of a sphere with radius 5 cm is r2. Then r1 =5r2

Step-by-step explanation:

Answer 2

The answer is r1 = 5r2.

Given,

The ratio of the surface area of a sphere to that of its volume with radius 1 cm = r1

The ratio of the surface area of a sphere to that of its volume with radius 5 cm = r2

To find,

The value of r1 in terms of r2.

Solution,

The value of r1 in terms of r2 will be r1 = 5r2.

We can easily solve this problem by following the given steps.

We know that the formula to find the surface area of a sphere is 4πr² and to find its volume is 4/3 πr³.

According to the question,

The ratio of the surface area of a sphere to that of its volume with radius 1 cm = r1

4πr² ÷ 4/3πr³ = r1

Putting the value of r as 1 cm,

4π(1)² ÷ 4/3π(1)³ = r1

4π ÷ 4/3π = r1

3×4π ÷ 4π = r1

3 = r1 ---- equation 1

Now, in the second case when r is 5 cm,

4πr² ÷ 4/3πr³ = r2

4π(5)² ÷ 4/3π(5)³ = r2

4π (25) ÷ 4/3π (125) = r2

Dividing the numerator and denominator by 25,

4π ÷ 4/3π (5) = r2

3×4π ÷ 4π (5) = r2

3/5 = r2

Using the cross multiplication method,

3 = 5r2

Putting the value of 3 from equation 1,

3 = 5r2

r1 = 5r2

Hence, the value of r1 in terms of r2 is r1 = 5r2.