Answer:
Surface area = 80.4 cm²
Step-by-step explanation:
The diagram of both cylinders is attached below for a better understanding.
Surface area = 2πrh + 2πr²
236 = 2(3.14)(5)r + 2(3.14)r²
236 = 31.4r + 6.28r²
236 = 6.28(r² + 5r)
35.58 = r² + 5r
r = 3.97 cm
Two cylinders are in proportion if their heights and radius are in proportion:
Ratio of height of small cylinder to big cylinder = 3/5 = 0.6
So ratio of radius of both is also 0.6
Let R be the radius of small cylinder
ratio of radius of small cylinder to big cylinder = R / 3.97
R = (0.6)(3.97)
R = 2.38
R = 2.38cm and h = 3 cm
Surface area = 2πrh + 2πr²
Surface area = 2(3.14)(2.38)(3) + 2(3.14)(2.38)²
Surface area = 80.4115cm²
Round of to nearest tenth
Surface area = 80.4 cm²
