Question

These cylinders are similar. Find the surface area of the smaller cylinder. Round to the nearest tenth.

Answer 1

Answer:

Surface area = 80.4 cm²

Step-by-step explanation:

The diagram of both cylinders is attached below for a better understanding.

First find the radius of larger cylinder:

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

Find the radius of Smaller cylinder:

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

Surface Area for small cylinder:

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