Question

12. Find the ratio between the total surface area of a cylinder to its curved surface a
given that its height and radius are 7.5 cm and 3.5 cm
​

Answer 1

✬ Ratio = 22 : 15 ✬

Step-by-step explanation:

Given:

• Height of cylinder is 7.5 cm.
• Radius of cylinder is 3.5 cm.

To Find:

• Ratio between TSA and CSA

Solution: As we know that

★ CSA of Cylinder = 2πrh ★

➮ 2 $\times$ 22/7 $\times$ 3.5 $\times$ 7.5

➮ 44/7 $\times$ 26.25

➮ 44 $\times$ 3.75

➮ 165 cm²

★ TSA of Cylinder = 2πr (h + r) ★

➮ 2 $\times$ 22/7 $\times$ 3.5 (7.5 + 3.5)

➮ 44/7 $\times$ 3.5 $\times$ 11

➮ 44 $\times$ 0.5 $\times$ 11

➮ 242 cm²

∴ Ratio = TSA/CSA

➯ Ratio = 242/165 = 22 : 15

Hence, required ratio is 22 : 15.

Answer 2

Given :

• Height of cylinder = 7.5 cm
• Radius of cylinder = 3.5 cm

To find :

• Ratio between the total surface area to curved surface area of the cylinder.

Solution :

Formula Used :-

★ ${\boxed{\sf{TSA\:of\: cylinder=2\pi\:r(h+r)}}}$

★ ${\boxed{\sf{CSA\:of\: cylinder=2\pi\:rh}}}$

Here,

• Height = h
• Radius = r

TSA of cylinder = 2πr(h+r)

→ TSA of cylinder = 2π×3.5(7.5+3.5) cm²

→ TSA of cylinder = 2π×3.5×11 cm²

→ TSA of cylinder = 2π × 38.5 cm²

CSA of cylinder = 2πrh

→ CSA of cylinder = 2π × 3.5×7.5 cm²

→ CSA of cylinder = 2π × 26.25 cm²

Now,

TSA of cylinder : CSA of cylinder

→ 2π × 38.5 : 2π × 26.25

→ 38.5 : 26.25

→ 154 : 105

→ 22 : 15

Therefore, the ratio of the TSA to CSA of cylinder is 22 : 15.