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Question 30 Mensuration Exercise 17.1

The total surface area of a cylinder is 352 cm^{2} . If its height is 10 cm, then find the diameter of the base.

Answer:

**Solution:**

The area of the cylinder is determined by adding the areas of its two circular bases and curving surface.

Total surface area of the cylinder = 353 cm^{2}

Height, h = 10 cm

2π r(r+h) = 352

2×(22/7)×r×(r+10) = 352

r^{2}+10r = (352×7)/2×22

r^{2}+10r = 56

r^{2}+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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