Mensuration Exercise 15.5 – Questions A petrol tank is in the shape of a cylinder with hemisphere of same radius attached to both ends. If the total length of the tank is 6m and the radius is 1m, what is the capacity of the tank in litres. A rocket is in the shape of a… Continue reading Mensuration Exercise 15.5 – Class 10 – Solutions

# Tag: Karnataka state syllabus mathematics class VIII

## Ratio and Proportion – Full Chapter – Class IX

After studying the chapter Ratio and Proportion and their general form; to understand and differentiate between different types of proportion; to acquire skills of writing proportion; to solve problems on time and work involving proportions; to apply proportion in day to day life situations. 2.4.1 Introduction to Ratio and Proportion In a ratio a :… Continue reading Ratio and Proportion – Full Chapter – Class IX

## Cube Root – Ch.2 – cubes and cube roots – Class VIII

If N is number and n is another number such that N = n3, we say n is the cube root of N and write n = cube root of N . i.e., Examples for Cube root Example 12: Find the cube root of 216 by factorization. Solution: 216 = 2 x (108) = 2 x 2… Continue reading Cube Root – Ch.2 – cubes and cube roots – Class VIII

## Perfect cubes – Chapter 2- Class VIII

Let, 1 = 1 x 1 x 1; 8 = 2 x 2 x 2; 27 = 3 x 3 x 3; 125 = 5 x 5 x 5; We observe that, each number is written as a product of 3 equal integers. We say that an integer N is a perfect cube if N… Continue reading Perfect cubes – Chapter 2- Class VIII

## Perfect squares near to a given number – chapter 2

Examples to find perfect squares near to a given number Example 5: If the area of a square is 90 cm2, what is its side-length rounded to the nearest integer? Solution: Since, area A = a2, we have a2 = 90. But 81 < 90 < 100 and 81 is the nearer to 90 than… Continue reading Perfect squares near to a given number – chapter 2

## Square root of a perfect square by factorization – Chapter 2

Examples for Square root of a perfect square by factorization Example 1: Find the square root of 5929. Solution: Thus, 7 x 7 x 11 x 11 = 5929 Therefore, [group it] (7 x 11) x (7 x 11) = 77 x 77 = 772 = 5929. Example 2: Find the square root of 6724. Solution:… Continue reading Square root of a perfect square by factorization – Chapter 2

## 1.2.2 Perfect squares – Chapter 2 – Class VIII

Observe that, 1 = 1, 4 = 2 x 2, 9 = 3 x 3, 100 = 10 x 10. If a is an integer and b = a x a, we say b is a perfect square. Hence 1, 4, 9, 16, 25 are all perfect squares. Since 0 = 0 x 0, we… Continue reading 1.2.2 Perfect squares – Chapter 2 – Class VIII

## Divisibility tests – Playing with Numbers

If a number ends with any of the digits 0, 2, 4, 6, or 8, you immediately say the number is divisible by 2. Why? We write any such number a as a = 10k + r, where r is the remainder when divided by 10. Hence r is one of the numbers 0, 2,… Continue reading Divisibility tests – Playing with Numbers

## Mensuration – Class VIII

A solid occupies fixed amount of space. Solids occur in different shapes. Observe the following shapes. These shapes (cuboid, cube, triangular prism, cylinder, cone etc) are known as three dimensional objects. Surface area of cuboid- Mensuration Lateral Surface area of cuboid = 2h(l + b) Total surface area of cuboid = 2(lb +bh + lh) Here… Continue reading Mensuration – Class VIII

## Quadrilaterals – Full Chapter – Class VIII

A closed figure having four sides formed by joining four points, no three of which are collinear, in an order is called quadrilateral. For example: Quadrilateral is the union of four line segments that join four coplanar points; no three of which are collinear and each segment meet exactly two other lines, each at their… Continue reading Quadrilaterals – Full Chapter – Class VIII