Here you get the CBSE Class 10 Mathematics chapter 12, Surface Areas and Volumes: NCERT Exemplar Problems and Solutions, Exercise 12.3(Part-II). This part of the chapter includes solutions to questions numbered 8 to 14. This exercise comprises only the Short Answer Type Questions framed from various important topics in the chapter. Each question is provided with a detailed solution.
NCERT Exemplar problems are a very good resource for preparing the critical questions like Higher Order Thinking Skill (HOTS) questions. All these questions are very important to prepare for CBSE Class 10 Mathematics Board Examination 2017-2018 as well as other competitive exams.
Find below the NCERT Exemplar problems and their solutions for Class 10 Mathematics Chapter, Surface Areas and Volumes:
Short Answer Type Questions (Q. No. 8-14):
Question. 8 Two solid cones A and B are placed in a cylindrical tube as shown in the figure. The ratio of their capacities is 2:1. Find the height and capacities of cones. Also, find the volume of the remaining portion of the cylinder.
Given, the ratio of their capacities is 2:1.
So, let volume of Cone I be 2V and volume of Cone II be V.
Again, let height of the Cone I = h1 cm
Then height of Cone II = (21 - h1) cm
Given, diameter of the cones = 6cm
Question. 9 An ice-cream cone full of ice-cream having radius 5cm and height 10cm as shown in figure given below. Calculate the volume of ice-cream, provided that its 1/6 part is Left unfilled with ice-cream.
Given, ice-cream cone is the combination of a cone of radius 5 cm and height 10 cm and a hemisphere of radus 5 cm.
Question. 10 Marbles of diameter1.4cm are dropped into a cylindrical beaker of diameter 7cm containing some Water. Find the number of marbles that should be dropped into the beaker, so that the water level rises by 5.6cm.
When marbles are dropped in beaker containing some water, the volume of water raised in beaker will be equal to the volume of total marbles.
Question. 11 How many spherical lead shots each of diameter 4.2cm can be obtained from a solid rectangular lead piece with dimensions 66cm, 4cm and 21cm?
Hence, the required number of spherical lead shots is 1500.
Question. 12 How many spherical lead shots of diameter 4cm can be made out of a solid cube of lead whose edge measures 44cm.
Question. 13 A wall 24m long, 0.4m thick and 6m high is constructed with the bricks in each of the dimensions 25cm × 16cm × 10cm. If the mortar occupies 1/10th of the volume of the wall, then find the number of bricks used in constructing the wall.
Given, length of wall, l = 24m,
Thickness of wall, b = 0.4m, and
Height of wall, h = 6m
Hence, the required number of bricks used in constructing the wall is 12960.
Question. 14 Find the number of metallic circular disc with 1.5cm base diameter and of height 0.2cm to be melted to form a right circular cylinder of height 10 cm and diameter 4.5cm.
Given, height of each circular disc, i.e., a circular cylinder, h = 0.2cm
And diameter of each circular disc = 1.5cm