NCERT Solutions for Class 10 Maths Chapter 13

Important NCERT Questions

Surface areas and Volumes,

NCERT Books for Session 2022-2023

CBSE Board and UP Board Others state Board

EXERCISE 13.2

Page No:248

Questions No:7

# A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm.

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Radius of hemispherical part = Radius of conical part = Radius of cylindrical part = 60 cm

Height of cylindrical part (h1) = 180 cm, Height of conical part (h2) = 120 cm

Volume of water left in the cylinder

= Volume of cylinder – (Volume of hemisphere + Volume of cone)

= πr²h₁ – (2/3πr³ + 1/3πr²h₂) = π(60)² × 180 -[(2/3)π(60)³ + 1/3π(60)² × 120]

= π (60)² [180 – (40 + 40)] = 22/7 × 60 × 60 × 100

= 1131428.57 cm³ = 1.131 m³