The area of the curved surface of a cylinder is 1 000 cm2, and the diameter of the base is 20 cm.What is the best estimate of the volume of the cylinder?a6 000 cm2 b5 500 cm2c5 000 cm2 d4 000 cm2

To find the volume of a cylinder, we use the formula V = πr²h, where r is the radius and h is the height.

From the question, we know that the area of the curved surface of the cylinder (which is also known as the lateral surface area) is 1,000 cm². The formula for the lateral surface area of a cylinder is A = 2πrh.

We also know that the diameter of the base is 20 cm, so the radius r is 20/2 = 10 cm.

We can substitute the known values into the formula for the lateral surface area and solve for h:

1,000 = 2π(10)h 1,000 = 20πh h = 1,000 / (20π) ≈ 15.92 cm

Now we can substitute r = 10 cm and h ≈ 15.92 cm into the formula for the volume of a cylinder and solve for V:

V = π(10)²(15.92) ≈ 5,000 cm³

So, the best estimate for the volume of the cylinder is 5,000 cm³. Therefore, the correct answer is (c) 5,000 cm³.