Total surface area of cylinder=2πr(r+h)
=2×22/7×7(7+h)=968
=44×7+44×h=968
=308+44h=968
=44h=968-308=660
=h=660/44
=15

Problem: Find the height of a cylinder whose radius is 7 cm and the total surface area is 968cm2.

Solution:

To find the height of the cylinder, we need to use the formula for the total surface area of a cylinder. The formula for the total surface area of a cylinder is given by:

Total Surface Area = 2πr(r + h)

Where r is the radius of the cylinder and h is the height of the cylinder.

Using the given values, we have:

Total Surface Area = 968 cm²
Radius, r = 7 cm

Substituting these values in the formula above, we get:

968 = 2π * 7 * (7 + h)

Simplifying the equation, we get:

968 = 98π + 14πh

Subtracting 98π from both sides, we get:

968 - 98π = 14πh

Dividing both sides by 14π, we get:

h = (968 - 98π) / (14π)

Using a calculator to evaluate the right-hand side, we get:

h ≈ 5.5 cm

Therefore, the height of the cylinder is approximately 5.5 cm.

Answer: The height of the cylinder whose radius is 7 cm and the total surface area is 968 cm² is approximately 5.5 cm.