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If the cost of painting the surface of the cone is Rs. 5/m2 and cost of painting the flat surface is Rs.550 less than that of painting the curved surface. If the height of the cone is √95 cm, then what will be the slant height of the cone?

If the cost of painting the surface of the cone is Rs. 5/m2 and cost of painting the flat surface is Rs.550 less than that of painting the curved surface. If the height of the cone is √95 cm, then what will be the slant height of the cone? Correct Answer 12 cm

Given:

Cost of painting the surface of cone = Rs. 5/m2

Height of cone = √95

Formula used:

Area of cone = πrl

Area of circle = πr2

Calculation:

Cost of painting the curved surface of the cone = 5 × πrl = 5πrl

Cost of painting the flat surface of the cone = 5 × πr2 = 5πr2

According to the question:

5πrl – 5πr2 = 550

⇒ 5πr(l – r) = 550

⇒ r(l – r) = 35    ... (1)

⇒ l2 – r2 = (√95)2

⇒  (l – r)(l + r) = 95    ... (2)

From (1) and (2):

⇒ (l + r)/r = 19/7

⇒ 7l + 7r = 19r

⇒ 7l = 12r    ... (3)

From (1) and (3):

⇒ r(12r – 7r) = 35 × 7

⇒ 5r2 = 245

⇒ r = 7 cm

Now,

⇒ (l)2 = 95 + 49 = 144

⇒ l = 12 cm

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