Question 2 of 13intermediate🔧 ApplyNumerical3 marks

A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel.

Correct Answer

572 cm2cm^{2}

Exercise: EXERCISE 12.1 | Q: 2 | (Page Page 6)
For More Understanding

Explanation

The problem involves a combined solid: a hollow hemisphere mounted by a hollow cylinder. The inner surface area is the sum of the curved surface areas of the hemisphere (2πr2r^{2}) and the cylinder (2πrh). The radius is half the diameter (7 cm). The cylinder height is total height minus hemisphere radius (13-7=6 cm). Using π=22/7 gives 572 cm2cm^{2}, as per standard NCERT approach.

Solution Steps

  1. Step 1: Find radius: Diameter = 14 cm, so radius r = 14/2 = 7 cm.

  2. Step 2: Find height of cylinder: Total height = 13 cm. Height of hemisphere = r = 7 cm. Therefore, height of cylinder h = 13 - 7 = 6 cm.

  3. Step 3: Inner surface area formula: Inner surface area = CSA of hemisphere + CSA of cylinder = 2πr2r^{2} + 2πr h = 2πr(r + h).

  4. Step 4: Substitute and calculate: = 2 × (22/7) × 7 × (7 + 6) = 2 × (22/7) × 7×137 \times 13 = 2×222 \times 22 × 13 = 572 cm2cm^{2}.

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