Question

Two cylinders have the same surface area. The shorter of the two has a radius of 3 cm and the height of 2cm and the taller cylinder has a radius of 2 cm calculate:

1) The height of the taller cylinder is:
a) 14 b) 12 c) 13 d) 15

Answer 1

Answer: The surface area of a cylinder is given by the formula:

S = 2πr^2 + 2πrh

where r is the radius of the base, h is the height of the cylinder, and π is the mathematical constant pi.

Given that the two cylinders have the same surface area, we can set up an equation using the formula above for each cylinder and equate them.

For the shorter cylinder:

S = 2π(3)^2 + 2π(3)(2) = 36π

For the taller cylinder:

S = 2π(2)^2 + 2π(2)h = 8π + 4πh

Since the two cylinders have the same surface area, we can set the two equations equal to each other and solve for h:

8π + 4πh = 36π

Simplifying the equation:

4πh = 28π

Dividing both sides by 4π:

h = 7

Therefore, the height of the taller cylinder is 7 cm.

Answer: 7.

Explanation: