Maths-
General
Easy

Question

The volume of right circular cylinder A is 22 cubic centimeters. What is the volume, in cubic centimeters, of a right circular cylinder with twice the radius and half the height of cylinder A?

  1. 11
  2. 22
  3. 44
  4. 66

hintHint:

Hint:- The volume of a 3 -dimensional solid is the amount of space it occupies.
The volume V of a cylinder with radius r is the area of the base B times the height h .
V = Bh  or  V= πr2h

The correct answer is: 44


    Solution:-
    • We have given volume of a right circular cylinder(A), V1 = 22 cm3
    • Let R be radius of cylinder A  and H be the height.
    • Let the second cylinder denoted as cylinder B
    • We have to find the volume of the cylinder B whose radius is twice of cylinder A
    Let the radius of cylinder B be R2.
    So,           R2 = 2R    ---------(1)
    • Height of cylinder B is half of height of cylinder A.
    So,           H2 = H/2   ---------(2)
    • To find the volume of cylinder B we will have to compare the volumes of both cylinders. Let’s find equation of volume .
    • We know the volume of cylinder= πr2h
    • Volume of cylinder A = πR2H                     ----------(3)
    • Volume of cylinder B = πR22H2
    • Substitute the values of R2 and H2 from equation (1) and (2) in Volume of cylinder B formula.
    Volume of cylinder B = π(2R)2(H/2)
    = π (4R2)(H/2)
    = π (2R2)(H)
    Volume of cylinder B =  2πR2H                 ---------(4)
    • Divide the volume of cylinder A by volume of cylinder B from equation (3) and (4).
    Volume of cylinder A/ Volume of cylinder B = πR2H / 2πR2H
    Volume of cylinder A/ Volume of cylinder B = 1/ 2
    • We know the volume of cylinder A is 22 cm3.
    So, 22 / Volume of cylinder B = 1/ 2
    • Reciprocating both sides we get,
    Volume of cylinder B / 22  =  2
    • Multiplying both sides by 22 we get,
    Volume of cylinder B = 44 cm3
    • Therefore, the volume of second cylinder is option C) 44 .

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