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.
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