Question

A bus stop is barricaded from the remaining part of the road by using 50 hollow cones made of recycled card-board. Each cone has a base diameter of 40 cm and height 1 m. If the outer side of each of the cones is to be painted and the cost of painting is Rs. 12 per m^2, what will be the cost of painting all these cones ?
(Use pi = 3.14 and root 1.04 = 1.02)

Answer 1

$\huge\mathfrak{Solution:}$

From the question, h = 1 m and r = 20 cm = 20/100 m = 1/5 m

Suppose the slant height of the cone = l

l^2 = h^2 + r^2

= 1 + 1/25 = 26/25

= 26 × 4 / 100

= 104/100 = 1.04

Therefore, l = root 1.04 = 1.02 m

Now, curved surface area of the cone

= pi × r × l

= 3.14 × 1/5 × 1.02 m

Therefore, curved surface area of 50 cones

= pi × r × l × 50

= 3.14 × 1/5 × 1.02 × 50

= 3.14 × 1.02 × 10 m^2 = 3.14 × 10.2 m^2

Therefore, total cost of painting at the rate of Rs. 12 per m^2 = Rs. (3.14 × 1.02 × 10) × 12 = Rs. 384.34 (approx.)

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Answer 2

$\huge\mathfrak{Solution:}$

From the question, h = 1 m and r = 20 cm = 20/100 m = 1/5 m

Suppose the slant height of the cone = l

l^2 = h^2 + r^2

= 1 + 1/25 = 26/25

= 26 × 4 / 100

= 104/100 = 1.04

Therefore, l = root 1.04 = 1.02 m

Now, curved surface area of the cone

= pi × r × l

= 3.14 × 1/5 × 1.02 m

Therefore, curved surface area of 50 cones

= pi × r × l × 50

= 3.14 × 1/5 × 1.02 × 50

= 3.14 × 1.02 × 10 m^2 = 3.14 × 10.2 m^2

Therefore, total cost of painting at the rate of Rs. 12 per m^2 = Rs. (3.14 × 1.02 × 10) × 12 = Rs. 384.34 (approx.)

________________

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