Question

Express answers in terms of pi.

The radius of a cylinder is 10; the length is 2. Find:
a. circumference of the base.
b. area of the base.
c. L.A.
d. T.A.
e. V

Answer 1

a. The circumference of the base is 2πr, where r is the radius of the cylinder. Therefore, the circumference of the base is:

2π(10) = 20π

So the circumference of the base is 20π.

b. The area of the base is πr^2, where r is the radius of the cylinder. Therefore, the area of the base is:

π(10)^2 = 100π

So the area of the base is 100π.

c. The lateral area of the cylinder is given by the formula 2πrh, where r is the radius of the cylinder and h is the height (or length) of the cylinder. Therefore, the lateral area of the cylinder is:

2π(10)(2) = 40π

So the lateral area of the cylinder is 40π.

d. The total surface area of the cylinder is the sum of the lateral area and the areas of the two bases. The area of each base is πr^2, which we already calculated to be 100π. Therefore, the total surface area of the cylinder is:

2(100π) + 40π = 240π

So the total surface area of the cylinder is 240π.

e. The volume of the cylinder is given by the formula πr^2h, where r is the radius of the cylinder and h is the height (or length) of the cylinder. Therefore, the volume of the cylinder is:

π(10)^2(2) = 200π

So the volume of the cylinder is 200π.