A
Shahmeen bought her best friend a poster for a present and wants to wrap it up for her as a
surprise. Shahmeen rolls the poster up in a cylinder and has just enough wrapping paper to cover
the poster and the ends of the cylinder without the wrapping paper overlapping. How much
wrapping paper does Shahmeen have if the cylinder is 60 cm long and has a diameter of 4 cm?
B. Ms. Calculation, the math teacher, has an 80 cm long rain stick that makes a sound like running
water when she turns it upside down. When the students hear its sound, they know that it is a
signal for them to be attentive listeners. Her rain stick is made of a big piece of bamboo for the long
part of the cylinder and bamboo caps cover each end. It has a circumference of 22 cm. What is
the surface area of her bamboo rain stick?

A: 779 cm²

B: 1837 cm²

Step-by-step explanation:

For both problems, use the formula for surface area of a cylinder:

SA = 2πr² + 2πrh

2πr² is the two bases.

2πrh is the curved surface.

PROBLEM A

"the cylinder is 60 cm long" is h = 60.

If given diameter, you can find "r" by dividing it by 2. d = 2r

Given d = 4, then r = 2.

SA = 2πr² + 2πrh

SA = 2π2² + 2π2(60)

SA = 8π + 240π               Add

SA = 248π                       Exact answer

SA ≈ 779.114978             Answer on calculator

SA ≈ 779           Rounded answer

Remember to include the units.

The surface area is about 779 cm².

PROBLEM B

"80 cm long" h = 80.

"circumference of 22 cm". C = 22. Remember C = 2πr. Find "r".

C = 2πr

22 = 2πr

11 = πr

r ≈ 11/π

SA = 2πr² + 2πrh

SA = 2π(11/π)² + 22(80)       Substitute 2πr with the circumference.

SA ≈ 1837.030992            Answer on calculator

SA ≈ 1837               Rounded answer

Remember to include the units.

The surface area is about 1837 cm².