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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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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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1. (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.

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