Assume π = 22/7 , unless stated otherwise. Diameter of the base of a cone is 10.5 cm and its slant height is 10 cm. Find its curved surface area. Solution: r = 10.5/2 cm = 5.25 cm , l = 10 cm Curved surface area of the cone = πrl = 22/7 x 5.25… Continue reading Surface Area and Volumes – Exercise 13.3 – Class IX

# Tag: NCERT class 9 mathematics

## Surface Area and Volumes – Exercise 13.2 – Class IX

The curved surface area of a right circular cylinder of height 14 cm is 88cm2 . Find the diameter of the base of the cylinder. Solution: Given, h = 14 cm ; surface area = 88 cm2 Curved surface area of the cylinder = 2πrh 88 = 2 x 22/7 x r x 14 r… Continue reading Surface Area and Volumes – Exercise 13.2 – Class IX

## Surface Area and Volumes – Exercise 13.1 – Class IX

A plastic box 1.5 m long, 1.25 m wide and 65 cm deep is to be made. It is to be open 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 of sheet for it, if a sheet measuring… Continue reading Surface Area and Volumes – Exercise 13.1 – Class IX

## Heron’s Formula – Exercise 12.2 – Class IX

A park, in the shape of a quadrilateral ABCD, has ∠ C = 90, AB = 9 m, BC = 12 m, CD = 5 m and AD = 8 m. How much area does it occupy? Solution: Given: a park, in the shape of a quadrilateral ABCD, has ∠ C = 90, AB… Continue reading Heron’s Formula – Exercise 12.2 – Class IX

## Heron’s Formula – Exercise 12.1 – Class IX

A traffic signal board, indicating ‘SCHOOL AHEAD’, is an equilateral triangle with side ‘a’. Find the area of the signal board, using Heron’s formula. If its perimeter is 180 cm, what will be the area of the signal board? Solution: Each side of a triangle = a Perimeter of a triangle = 3a s =… Continue reading Heron’s Formula – Exercise 12.1 – Class IX

## Construction – Exercise 11.2 – Class IX

Construct a triangle ABC in which BC = 7cm, ∠B = 75° and AB + AC = 13 cm. Solution: Draw a line segment BC = 7 cm Make an ∠B = 75° i.e., ∠CBX = 75° Cut a line segment BX at D such that BD = AB + AC = 13 cm Join… Continue reading Construction – Exercise 11.2 – Class IX

## Construction – Exercise 11.1 – Class IX

Construct an angle of 90˚ at the initial point of a given ray and justify the construction. Solution: Construction: Draw a line ray AB with initial point A Taking A as a centre draw an arc XY with any radius intersecting the ray AB at P. Draw another arc with same radius by taking C… Continue reading Construction – Exercise 11.1 – Class IX

## Circles – Exercise 10.5 – Class IX

In Fig. 10.36, A,B and C are three points on a circle with centre O such that ∠ BOC = 30° and ∠ AOB = 60°. If D is a point on the circle other than the arc ABC, find ∠ADC. Solution: Since ABC is an arc of the circle with centre O, which makes… Continue reading Circles – Exercise 10.5 – Class IX

## Circles – Exercise 10.4 – Class IX

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: In ∆AOO’, AO2 = 52 = 25 AO’2 = 32 = 9 OO’2 = 42 = 16 AO’2 + OO’2 = 9 + 16 = 25 =… Continue reading Circles – Exercise 10.4 – Class IX

## Circles – Exercise 10.3 – Class IX

Draw different pairs of circles. How many points does each pair have in common? What is the maximum number of common points? Solution: Maximum number of points in common are two. Suppose you are given a circle. Give a construction to find its centre. Solution: Take points A, B and C on the circumference of… Continue reading Circles – Exercise 10.3 – Class IX