"Question 2 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?
Class 8 Mensuration Page 191"
Answers
Mensuration:
Mensuration is the branch of mathematics which concerns itself with the measurement of Lengths, areas & volume of different geometrical shapes or figures.
Surface area:
The surface area of a solid is the sum of the areas of the plane or curved faces of the solid.
It is measured in square units such as square centimetre (cm²) and square metre (m²).
Whenever we talk about a total surface area of a cylinder the cylinder must be closed at both the ends by two circular regions or it should be a cylindrical solid object.
Total surface area of a solid cylinder= curved surface area + sum of the areas of two circular ends of the cylinder
= 2πrh+ 2πr²
Total surface area of a solid cylinder= 2πr(h+r)
The lateral surface area of the curved surface area of a cylinder= 2πrh
Volume:
The volume of a solid figure is a space occupied by it.
Volume is measured in cubic units. The common units of volume and a corresponding units of length cubic millimetre (mm³), cubic centimetre (cm³), cubic metre (m³).
The Litre (L) is a unit commonly used for measuring the capacity of vessels or the volume of a liquid.
1 m³=1000000 cm³, 1 cm³ = 1000 mm³
1 cm³= 1 ml, 1 m³= 1000 l= 1 kl
Volume of a cylinder is equal to the area of its circular base × its height= π r²h
Volume of right circular cylinder= π r²h.
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Solution:
Radius of cylinder A is half of radius of cylinder B it means the radius of cylinder B is Greater . While finding the volume we need to square the radius & square of radius gives more value .
The volume of cylinder B is Greater then Volume of Cylinder A.
Diameter of cylinder A= 7 cm
Radius of cylinder A= 7/2 cm
Height of cylinder A= 14 cm
Volume of cylinder = πr2H
Volume of Cylinder A= (22/7)(7/2)² 14
= (22/ 7) (49/4)× 14
= 539 cm³
Diameter of cylinder B= 14 cm
Radius of cylinder B= 14/2=7 cm
Height of cylinder B= 7 cm
Volume of Cylinder B= (22/7)(7)2 7
= 22×49
=1078 m³
So Volume Of Cylinder B is greater than Volume
of cylinder A
Total Surface Area of Cylinder
= 2πr(r+H)
Total Surface Area of Cylinder A=
2×(22/7)×(7/2)(7/2 +14)
= 22((7+28)/2)
= 22(35)/2
= 11×35
= 385 cm²
Total Surface Area of Cylinder B= 2×(22/7)×(7)(7+7)
= 44 × 14
= 616 cm²
Hence, the surface area of Cylinder B is also greater
.
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Hope this will help you...
Answer
V. Of A = πrsqh
= 22/7 × 7/2 × 7/2 × 14
= 539 cm cube
V. Of B = πrsqh
= 22/7 × 7 × 7 × 7
= 1078 cm cube
Area of A = 2πrh(h+r)
= 385 cm sq
Area of B = 2πrh(h+r)
= 616 cm sq
So , area and volume of B is bigger ..