CBSE Class 10 Math Question Paper 2018 | Q21B

This 3 mark question that appeared in CBSE class 10 Math board question paper is an easy question from the chapter Surface Areas and Volumes. Knowing the formulae to compute the volume and curved surface area of cone is sufficient to answer this question.

Question 21B: A heap of rice is in the form of a cone of base diameter 24 m and height 3.5 m. Find the volume of the rice. How much canvas cloth is required to just cover the heap?

Video Explanation

Explanatory Answer | CBSE 2018 Maths Paper Q21B

Shape of heap of rice is a cone.
Base diameter = 24 m ∴ Base radius = 12 m
Height of the cone = 3.5 m = \\frac{7}{2})m

Part 1: Compute Volume of Cone

Volume of cone = \\frac{1}{3}) πr²h
Volume = \\frac{1}{3}) × \\frac{22}{7}) × 12 × 12 × \\frac{7}{2}) = 528 m³

Part 2: Compute Curved Surface Area (CSA) of Cone

Area of canvas cloth required to cover the heap = Curved surface area of cone = πrl
l - slant height of the cone
l = \\sqrt{{h}^{2} + {r}^{2}}) = \\sqrt{{{(\frac{7}{2}})^{2}} + {(\frac{24}{2}})^{2}}) = \\frac{1}{2}) \\sqrt{49 + 576})
l = \\frac{1}{2})\\sqrt625) = \\frac{25}{2})m

CSA = \\frac{22}{7}) × 12 × \\frac{25}{2}) = \\frac{3300}{7}) = 471.42 sq m