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Surface Areas and Volumes
CBSE 2026 Board Exam Set 1 (Code 30/1/1)
CBSE_BOARD_PYQ_2026_30_1_1
Grade 10
Question:
[Section D]
A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are $2.1$ m and $4$ m respectively, and the slant height of the top is $2.8$ m, find the area of the canvas used for making the tent. Also, find the cost of the canvas of the tent at the rate of ₹$500$ per m$^2$.
OR
A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is $2$ cm and the diameter of the base is $4$ cm. Determine the volume of the toy. (Take $\pi = 3.14$).
A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are $2.1$ m and $4$ m respectively, and the slant height of the top is $2.8$ m, find the area of the canvas used for making the tent. Also, find the cost of the canvas of the tent at the rate of ₹$500$ per m$^2$.
OR
A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is $2$ cm and the diameter of the base is $4$ cm. Determine the volume of the toy. (Take $\pi = 3.14$).
Step-by-Step Solution
Key Concept: Main: Canvas $= 2\pi r h + \pi r l = 44$ m$^2$. Cost $= 44 \times 500 = ₹22,000$. OR: Volume $= (1/3)\pi r^2 h + (2/3)\pi r^3 = 25.12$ cm$^3$.
[Main Question Solution]
Area $= 2\pi(2)(2.1) + \pi(2)(2.8) = 44$ m$^2$. Cost $= 44 \times 500 = ₹22,000$. [5.0 Marks]
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[OR Choice Question Solution]
Volume $= (1/3)\pi(2)^2(2) + (2/3)\pi(2)^3 = 25.12$ cm$^3$. [5.0 Marks]
Area $= 2\pi(2)(2.1) + \pi(2)(2.8) = 44$ m$^2$. Cost $= 44 \times 500 = ₹22,000$. [5.0 Marks]
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[OR Choice Question Solution]
Volume $= (1/3)\pi(2)^2(2) + (2/3)\pi(2)^3 = 25.12$ cm$^3$. [5.0 Marks]
Correct Answer: Main: Area = 44 m^2, Cost = ₹22,000 | OR: Volume = 25.12 cm^3
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