Question 7 of 13intermediate🔧 ApplyNumerical3 marks

From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest cm².

Correct Answer

18 cm²

Exercise: EXERCISE 12.1 | Q: 8 | (Page Page 7)
For More Understanding

Explanation

This question involves finding the total surface area of a remaining solid after a conical cavity is hollowed out from a cylinder. The key insight is that the total surface area consists of three parts: the curved surface area of the cylinder (outer surface), the curved surface area of the cone (inner surface of the cavity), and the area of the circular base. The slant height of the cone must be calculated using the Pythagorean theorem before finding its curved surface area.

Solution Steps

  1. Given: Height (h) = 2.4 cm, Diameter = 1.4 cm, Radius (r) = 0.7 cm

  2. Step 1: Find slant height of cone: l = r2+h2\sqrt{r² + h²} = 0.72+2.42\sqrt{0.7² + 2.4²} = 0.49+5.76\sqrt{0.49 + 5.76} = 6\sqrt{6}.25 = 2.5 cm

  3. Step 2: Calculate CSA of cylinder = 2πrh = 2 × (22/7) × 0.7×2.40.7 \times 2.4 = 10.56 cm²

  4. Step 3: Calculate CSA of cone = πrl = (22/7) × 0.7×2.50.7 \times 2.5 = 5.5 cm²

  5. Step 4: Calculate Area of base = πr² = (22/7) × 0.7² = (22/7) × 0.49 = 1.54 cm²

  6. Step 5: Total Surface Area = 10.56 + 5.5 + 1.54 = 17.6 cm² ≈\approx 18 cm² (to nearest cm²)

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