An Important Question of class 10 Based on Mensuration Chapter of M.L Aggarwal for ICSE BOARD.
(i)Here the sum of the radius and the height of a cylinder and the total surface area of the cylinder is given.
Find the height and the volume of the cylinder
(ii)If The total surface area of a cylinder and its height is given, then find the diameter of the base.
This is the Question Number 14, Exercise 17.1 of M.L Aggarwal.
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(i) The sum of the radius and the height of a cylinder is 37 cm and the total surface area of the cylinder is 1628 cm2 . Find the height and the volume of the cylinder. (ii) The total surface area of a cylinder is 352 cm2 . If its height is 10 cm, then find the diameter of the base.
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(i) Let r be the radius and h be the height of the cylinder.
Given the sum of radius and height of the cylinder, r+h = 37 cm
Total surface area of the cylinder = 1628 cm2
2r(r+h) = 1628
2×(22/7)×r×37 = 1628
r = (1628×7)/(2×22×37)
r = 7 cm
We have r+h = 37
7+h = 37
h = 37-7 = 30 cm
Volume of the cylinder, V = r2h
= (22/7)×72×30
= (22/7)×49×30
= 4620 cm3
Hence the height and volume of the cylinder is 30 cm and 4620 cm3 respectively.
(ii) Total surface area of the cylinder = 353 cm2
Height, h = 10 cm
2r(r+h) = 352
2×(22/7)×r×(r+10) = 352
r2+10r = (352×7)/2×22
r2+10r = 56
r2+10r-56 = 0
(r+14)(r-4) = 0
r+14 = 0 or r-4 = 0
r = -14 or r = 4
Radius cannot be negative. So r = 4.
Diameter = 2×r = 2×4 = 8 cm.
Hence the diameter of the base is 8 cm.