Question 34 (Choice 2) - CBSE Class 10 Sample Paper for 2024 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

Last updated at April 16, 2024 by Teachoo

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, 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 βΉ 500 per m^2.

This question is similar to Ex 12.1, 7 – Chapter 12 Class 10

Area of the canvas
= Curved surface area of cone + Curved surface area of the cylinder
Curved surface area of cone
Radius of cone = Radius of cylinder = r = 14 cm
Height of cone = h = Total height β Height of cylinder
= 13.5 β 3
= 10.5 m
Finding Slant Height
π = β(β^2+ π^2 )
π = β(γππ.πγ^π+ γππγ^π )
π = β(110.25+196)
π = β306.25
π = 17.5 m
Now,
Curved surface area of the cone = πππ
= 22/7 Γ 14 Γ 17.5
= 22 Γ 2 Γ 17.5
= 770 m2
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 Γ ππ/π Γ ππ Γ π
= 2 Γ 22 Γ 2 Γ 3
= 264γ πγ^π
Hence,
Area of the canvas
= Curved area of cone + Curved surface area of cylinder
= 770 + 264
= 1034 m2
Now, from questionβ¦
Keeping a provision of 26 π^π of canvas for stitching and wastage. Also, find the cost of the canvas to be purchased at the rate of βΉ 500 per π^2.
Total area of canvas to be purchased = 1034 + 26
= 1060 γ πγ^π
Finding Cost
Cost of the canvas of the tent for 1γ πγ^2 = Rs 500
Cost of the canvas of the tent for 1060γ πγ^2 = 500 Γ 1060
= Rs 5,30,000
Hence,
Total cost = Rs 5,30,000

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo

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