Chapter 13 Surface Areas and Volumes Ex 13.4 eng
Chapter 13 Surface Areas and Volumes Ex 13.4 Question 1. Find the surface area of a sphere of radius (i) 10.5 cm (ii) 5.6 cm (iii) 14 cm Solution: (i) We have, r = 105 cm Question 2. Find the surface area of a sphere of diameter (i) 14 cm (ii) 21 cm (iii) 3.5 […]
Chapter 13 Surface Areas and Volumes Ex 13.3 eng
Chapter 13 Surface Areas and Volumes Ex 13.3 Question 1. Diameter of the base of a cone is 10.5 cm and its slant height is 10 cm. Find its curved surface area. Solution: Question 2. Find the total surface area of a cone, if its slant height is 21 m and diameter of its base […]
Chapter 13 Surface Areas and Volumes Ex 13.2 eng
Chapter 13 Surface Areas and Volumes Ex 13.2 Question 1. The curved surface area of a right circular cylinder of height 14 cm is 88 cm2. Find the diameter of the base of the cylinder. Solution: We have, height = 14 cm Curved surface area Of a right circular cylinder = 88 cm2 r = […]
Chapter 13 Surface Areas and Volumes Ex 13.1 eng
Chapter 13 Surface Areas and Volumes Ex 13.1 Question 1. A plastic box 1.5 m long, 1.25 m wide and 65 cm deep is to be made. It is opened at the top. Ignoring the thickness of the plastic sheet, determine (i) The area of the sheet required for making the box. (ii) The cost […]
Chapter 12 Constructions Ex 12.2 eng
Chapter 12 Constructions Ex 12.2 Question 1. Construct a ∆ ABC in which BC = 7 cm, ∠B = 75° and AB + AC = 13 cm. Solution: Given that, in ∆ ABC, BC = 7 cm, ∠B = 75° and AS + AC = 13 cm Steps of construction Draw the base BC = […]
Chapter 12 Constructions Ex 12.1 eng
Chapter 12 Constructions Ex 12.1 Question 1. Construct an angle of 90° at the initial point of a given ray and justify the construction. Solution: Steps of construction Justification (i) Join BC. Then, OC=OB = BC (By construction) ∴ ∆COB is an equilateral triangle. ∴ ∠COB = 60° ∴ ∠EOA = 60° (ii) Join CD. […]
Chapter 11 Circles Ex 11.6 eng
Chapter 11 Circles Ex 11.6 Question 1. Prove that the line of centres of two intersecting circles subtends equal angles at the two points of intersection. Solution: Given: Two circles with centres O and O’ which intersect each other at C and D. To prove: ∠OCO’ = ∠ODO’ Construction: Join OC, OD, O’C and O’D Proof: In ∆ OCO’and […]
Chapter 11 Circles Ex 11.5 eng
Chapter 11 Circles Ex 11.5 Question 1. In figure A,B and C are three points on a circle with centre 0 such that ∠BOC = 30° and ∠ AOB = 60°. If D is a point on the circle other than the arc ABC, find ∠ ADC. Solution: Question 2. A chord of a circle […]
Chapter 11 Circles Ex 11.4 eng
Chapter 11 Circles Ex 11.4 Question 1. Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centres is 4 cm. Find the length of the common chord. Solution: Let O and O’ be the centres of the circles of radii 5 cm and 3 cm, respectively. […]
Chapter 11 Circles Ex 11.3 eng
Chapter 11 Circles Ex 11.3 Question 1. Draw different pairs of circles. How many points does each pair have in common? What is the maximum number of common points? Solution: Different pairs of circles are (i) Two points common (ii) One point is common (iii) No point is common (iv) No point is common (v) […]