A hemispherical dome of a building needs to be painted. If the circumference of the base of the dome is 154 cm, then find the cost of painting it if the cost of painting is Rs. 4 per 100 cm² (use π = \(\frac{22}{7}\)).

Question

Question

This question was previously asked in

SSC CHSL Exam 2023 Tier-I Official Paper (Held On: 10 Aug, 2023 Shift 4)

Answer 1

Given:

Circumference of the base of dome = 154 cm

Rate of painting = Rs.4/100cm²

Concept used:

Circumference of circle = 2 × π × r

Curved surface area of hemisphere = 2 × π × r²

Calculation:

Circumference of the base of dome = 154 cm

⇒ 2 × π × r = 154

⇒ 2 × (22/7) × r = 154

⇒ r = (154 × 7)/44

⇒ r = 49/2

Curved surface area of hemispherical dome = 2 × π × r²

⇒ 2 × π × r × r

⇒ 154 × (49/2)

⇒ 77 × 49 = 3773 cm²

The rate of painting of 3773 cm² = (4 × 3773)/100

⇒ Rs.150.92

∴ The correct answer is Rs.150.92.

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