A petrol tank is in the form of a frustum of a cone of height 20 m with diameters of its lower and upper ends as 20 m and 50 m respectively. Find the cost of petrol which can fill the tank completely at the rate of Rs. 70 per litre. Also find the surface area of the tank.

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Note : This is similar to Ex 13.4, 4 of NCERT – Chapter 13 Class 10

Check the answer here https://www.teachoo.com/1915/554/Ex-13.4--4---A-container--opened-from-top-and-made-up-of/category/Ex-13.4/

  1. Class 10
  2. Solutions of Sample Papers for Class 10 Boards

Transcript

Question 38 (OR 1st question) A petrol tank is in the form of a frustum of a cone of height 20 m with diameters of its lower and upper ends as 20 m and 50 m respectively. Find the cost of petrol which can fill the tank completely at the rate of Rs. 70 per litre. Also find the surface area of the tank. In order to find Cost of petrol, we need to find volume (in litres) Volume of container = Volume of frustum = 1/3 𝜋ℎ(𝑟12+𝑟22+𝑟1𝑟2) Here h = height = 20 m r1 = radius of upper end = 25 m r2 = radius of lower end = 10 m Volume of container = 1/3 𝜋ℎ(𝑟12+𝑟22+𝑟1𝑟2) = 1/3×3.14×20×(252+〖10〗^2+25×10) = (3.14 × 20)/3 (625 + 100 + 250) = (3.14 × 20)/3 × 975 = 3.14 × 20 × 325 = 20410 m3 = 20410 × 1000 litre = 2,04,10,000 litre Now , Cost of 1 litre petrol = Rs 70 Cost of 2,04,10,000 litre petrol = Rs 70 × 20410000 1 m3 = 1000 litre = Rs 1428700000 Now, We need to find surface area of tank Surface Area of tank = Area of frustum = 𝜋(𝑟1+𝑟2)𝑙 Here, r1 = 20 cm , r2 = 8 cm We need to find l We know that 𝑙 = √(ℎ2+(𝑟1−𝑟2)2) 𝑙 = √(202+(25−10)2) 𝑙 = √(202+(15)2) 𝑙 = √(400+225) 𝑙 = √625 𝑙 = √(〖25〗^2 ) 𝑙 = 25 cm Area of frustum = 𝜋(𝑟1+𝑟2)𝑙 = 3.14 × (25+10)×25 = 3.14 × 35×25 = 2747.5 cm2

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.