# Diameter of cylinder A is 7 cm, and the height is 14 cm. Diameter of cylinder B is 14 cm and height is 7 cm. Without doing any calculations can you suggest whose volume is greater? Verify it by finding the volume of both the cylinders. Check whether the cylinder with greater volume also has greater surface area?

**Solution:**

From the diagram, the radius of cylinder A is half of cylinder B, so the volume of cylinder A will be lesser than that of cylinder B.

Let us verfy the answer:

Radius of cylinder A(r) = 7/2 cm = 3.5 cm

Height of cylinder A(h) = 14 cm

Volume of cylinder A = πr²h = 22/7 × 3.5 × 3.5 × 7 = 269.5 cm³

Radius of cylinder B (r₁) = 14/2 cm = 7 cm

Height of cylinder B (h₁) = 7 cm

Volume of cylinder B = πr₁²h₁ = 22/7 × 7 × 7 × 7 = 1078 cm³

CSA of cylinder A = 2πrh = 2 × 22/7 × 3.5 × 14 = 308 cm²

Total surface area (TSA) of cylinder A = 2πr (r + h)

= 2πr² + 2πrh

= [2 × 22/7 × 3.5 × 3.5] cm² + 308 cm²

= 385 cm²

CSA of cylinder B = 2πr₁h₁ = 2 × 22/7 × 7 × 7 = 308 cm²

Total surface area (TSA) of cylinder B = 2πr₁ (r₁ + h₁)

= 2πr₁²h₁ + 2πr₁h₁

= (2 × 22/7 × 7 × 7) cm² + 308 cm

= 308 cm² + 308 cm²

= 616 cm²

The curved surface area of both cylinders will be the same, but the total surface area will be greater in the cylinder with a greater radius. Thus, the cylinder B has a greater volume as well as greater surface area.

**☛ Check: **NCERT Solutions for Class 8 Maths Chapter 11

**Video Solution:**

## Diameter of cylinder A is 7 cm, and the height is 14 cm. Diameter of cylinder B is 14 cm and height is 7 cm. Without doing any calculations can you suggest whose volume is greater? Verify it by finding the volume of both the cylinders. Check whether the cylinder with greater volume also has greater surface area?

Maths NCERT Solutions Class 8 Chapter 11 Exercise 11.4 Question 2

**Summary:**

Diameter of cylinder A is 7 cm, and the height is 14 cm. Diameter of cylinder B is 14 cm and height is 7 cm. Without doing any calculations we can say that the volume of cylinder B is greater as it has a greater radius. Volume of cylinder A is 269.5 cm³ and volume of cylinder B is 1078 cm³. The cylinder with greater volume also has a greater surface area as we have seen that cylinder B has a greater volume as well as greater surface area.

**☛ Related Questions:**

- Find the height of a cuboid whose base area is 180 cm² and volume is 900 cm³?
- A cuboid is of dimensions 60 cm × 54 cm × 30 cm. How many small cubes with side 6 cm can be placed in the given cuboid?
- Find the height of the cylinder whose volume is 1.54 m³ and diameter of the base is 140 cm?
- A milk tank is in the form of cylinder whose radius is 1.5 m and length is 7 m. Find the quantity of milk in litres that can be stored in the tank?

visual curriculum