Question 34 (a) - CBSE Class 10 Sample Paper for 2027 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

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Question 34 (a) A tent is in the shape of a cylinder surmounted by a conical top. If the height and radius of the cylindrical part are 3 m and 14 m respectively, and the total height of the tent is 13.5 m, then find the area of the canvas required for making the tent, keeping a provision of 26 m^(2) of canvas for stitching and wastage. Also, find the cost of the canvas to be purchased at the rate of ₹ 250 per m^(2). Now, Area of the canvas = Curved surface area of cone + Curved surface area of the cylinder 14 m 3 m 13.5 m 10.5 m Curved surface area of cone Radius of cone = Radius of cylinder = r = 14 cm Height of cone = h = Total height – Height of cylinder = 13.5 – 3 = 10.5 m Finding Slant Height 𝑙 = sqrt(ℎ^(2)+ 𝑟^(2)) 𝒍 = sqrt(𝟏𝟎.𝟓^(𝟐)+ 𝟏𝟒^(𝟐)) 𝑙 = sqrt(110.25+196) 𝑙 = sqrt(306.25) 𝒍 = 17.5 m 14 m 3 m 13.5 m 10.5 m Now, Curved surface area of the cone = 𝜋𝑟𝑙 = (22)/(7) × 14 × 17.5 = 22 × 2 × 17.5 = 770 m^(2) Curved surface area of the cylinder Radius of cylinder = r = 14 m Height of cylinder = h = 3 m Curved surface area of cylinder = 2𝜋rh = 2 × (𝟐𝟐)/(𝟕) × 𝟏𝟒 × 𝟑 = 2 × 22 × 2 × 3 = 264 𝒎^(𝟐) 14 m 3 m 13.5 m 10.5 m Hence, Area of the canvas = Curved area of cone + Curved surface area of cylinder = 770 + 264 = 1034 m^(2) Now, from question… Keeping a provision of 26 𝒎^(𝟐) of canvas for stitching and wastage. Also, find the cost of the canvas to be purchased at the rate of ₹ 250 per 𝑚^(2). Total area of canvas to be purchased = 1034 + 26 = 1060 𝒎^(𝟐) Finding Cost Cost of the canvas of the tent for 1 𝑚^(2) = Rs 250 Cost of the canvas of the tent for 1060 𝑚^(2) = 250 × 1060 = Rs 2,65,000 Hence, Total cost = Rs 2,65,000