A conical cap has the base diameter 24 cm and height 16 cm. What is the cost of painting the surface of the cap at the rate of 70 paisa per square cm?

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SSC CHSL Memory Based Test (Held on: 14 August 2023 Shift 1)

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Answer 1

Given

Diameter of conical cap = 24 cm

Height of conical cap = 16 cm

Formula used

Curved surface area of cone = πrl

l² = r² + h²

Where, l = slant height of the cone

r = radius of the cone

h = height of the cone

Calculation

Diameter of conical cap = 24 cm

Radius of conical cap = 12 cm

Now, l2 = r2 + h²

⇒ l² = (12² + 16²)

⇒ l² = (144 + 256)

⇒ l² = 400 cm²

⇒ l = 20 cm

The curved surface area of the cone = πrl

⇒ (\(\frac{22}{{7}}\) × 12 × 20) cm²

⇒ \(\frac{5280}{{7}}\) cm²

The cost of painting the surface of the cap

⇒ Rs. (\(\frac{5280}{{7}}\) × 70/100) [1 rupee = 100 paisa]

⇒ Rs. 528

∴ The cost of painting the surface of the cap is Rs. 528.