Identify the lateral area and the surface area of the cylinder rounded to the nearest tenth.

Question

A right cylinder has a circumference of 14π cm. Its height is 3 times the radius. Identify the lateral area and the surface area of the cylinder rounded to the nearest tenth.

I have been working on this and I cannot figure it out.

Answer 1

if you could cut the cylinder and fold it flat it would look like a rectangle whose length is the circumference which is 14∏

C=∏d

C=14∏, so d=14 cm and r=7 cm

the height is 3*7=21 cm

the width of the rectangle is the height which is 21 cm

the lateral area is l*w=14∏*21=294∏ sq cm

294∏=294*3.14159=923.627 sq cm

the surface area includes the two circles on the top and on the bottom

A=∏r²

A=∏*7²

A=49∏

there are 2 circles so 2*49∏=98∏

98∏=98*3.14159=307.875 sq cm

the surface area=923.627+307.875=1231.5 sq cm or 98∏+294∏=392∏ sq cm

Answer 2

C= 2πr

14π=2πr

r = 7 cm

h = 3r = 3(7)

h = 21 cm

LA = 2πrh = 2π(7)(21)

LA = 294π ≈ 923.6 cm²

SA = 2πr² + 2πrh = 2π(7)² + 294π = 98π + 294π

SA = 392π ≈ 1231.5 cm²