Question

The curved surface area of a solid

cylinder is 660 cm2
.

The cylinder has height 10 cm.
a) What is the circumference of the
cylinder?
b) What is the radius of the cylinder?
c) What is the area of one circular
base?
d) What is the surface area of the
cylinder?

Answer 1

b) The circumference of the cylinder is approximately 207 cm. c) The area of one circular base is approximately 3421 cm². d) The surface area of the cylinder is approximately 7502 cm².

Step-by-step explanation:

b) To find the circumference of the cylinder, we can use the formula C = 2πr. Since the curved surface area is given as 660 cm², we can calculate the radius using the formula A = 2πrh, where A is the curved surface area and h is the height. Substituting the given values, we get 660 cm² = 2πr(10 cm), which gives us r = 33 cm. Plugging this value back into the formula for circumference, we get C = 2π(33 cm) ≈ 207 cm.

c) The area of one circular base of the cylinder can be found using the formula A = πr². Substituting the value of the radius (33 cm), we get A = π(33 cm)² ≈ 3421 cm².

d) The surface area of the cylinder can be calculated by summing the areas of the two circular bases and the curved surface. We know the area of one circular base is approximately 3421 cm². The curved surface area is given as 660 cm². So, the total surface area is 2(3421 cm²) + 660 cm² = 7502 cm².

Answer 2

a) The circumference of the cylinder can be found using the formula C = 2πr, where r is the radius of the circular base. Rearranging the formula, we get r = C/2π. To find the circumference, we can use the formula for the curved surface area: A = 2πrh, where h is the height of the cylinder. Substituting the given values, we get:

660 = 2πr(10)

r = 33/π

Now we can find the circumference:

C = 2πr = 2π(33/π) = 66

Therefore, the circumference of the cylinder is 66 cm.

b) The radius of the cylinder is given by r = 33/π, which we already found in part a).

c) The area of one circular base can be found using the formula A = πr^2. Substituting the value of r from part b), we get:

A = π(33/π)^2 = 1089/π

Therefore, the area of one circular base is 1089/π cm^2.

d) The surface area of the cylinder consists of the curved surface area and two circular bases. The area of one circular base was found in part c), so we just need to add the curved surface area to twice the area of one circular base:

Surface area = 2A + 2πrh

Substituting the given values, we get:

Surface area = 2(1089/π) + 2π(33/π)(10) = 2187/π + 660

Therefore, the surface area of the cylinder is 2187/π + 660 cm^2.

Step-by-step explanation: