CBSE Class 10 Math Question Paper 2016 | Q12

The given question is a medium difficulty 3-mark question from the chapter Surface Areas and Volumes. Concept Tested: Computing curved surface areas of a cone and a cylinder. This question appeared in Section C of the 2016 CBSE class 10 board paper.

Question 12: A tent is in the shape of a cylinder surmounted by a conical top of same diameter. If the height and diameter of cylindrical part are 2.1 m and 3 m respectively and the slant height of conical part is 2.8 m, find the cost of canvas needed to make the tent if the canvas is available at the rate of ₹ 500/sq.metre. (Use π = \\frac{22}{7}).

Video Explanation

Explanatory Answer | CBSE 2016 Maths Paper Q12

Cost of Canvas = Area of Canvas × cost per sqm.
The tent is in the shape of a cylinder with a conical top.
Area of Canvas = Curved surface area of cylinder + Curved surface area of cone

Step 1: Compute Curved Surface Area of Cylinder

Curved surface area of cylinder = 2 πrh
= 2 × \\frac{22}{7}) × \\frac{3}{2}) × 2.1 = \\frac{99}{5})

Step 2: Compute Curved Surface Area of Cone

Curved surface area of cone = πrl
= \\frac{22}{7}) × \\frac{3}{2})× 2.8 = \\frac{66}{5})

Area of Canvas = \\frac{99}{5}) + \\frac{66}{5}) = \\frac{165}{5}) = 33 sqm

Step 3: Compute Cost of Canvas

Cost of Canvas = 33 × 500 = ₹ 16,500