Secondary School (English Medium) (5 to 8) Class 8 - CBSE Question Bank Solutions

A metal sheet 27 cm long, 8 cm broad and 1 cm thick is melted into a cube. The side of the cube is ______.

Three cubes of metal whose edges are 6 cm, 8 cm and 10 cm respectively are melted to form a single cube. The edge of the new cube is ______.

Two cubes have volumes in the ratio 1 : 64. The ratio of the area of a face of first cube to that of the other is ______.

A cube of side 4 cm is painted on all its sides. If it is sliced in 1 cubic cm cubes, then number of such cubes that will have exactly two of their faces painted is ______.

A cube of side 5 cm is cut into 1 cm cubes. The percentage increase in volume after such cutting is ______.

If a cube fits exactly in a cylinder with height h, then the volume of the cube is ______ and surface area of the cube is ______.

If the length of each edge of a cube is tripled, what will be the change in its volume?

How many cubes each of side 0.5 cm are required to build a cube of volume 8 cm³?

A wooden box (including the lid) has external dimensions 40 cm by 34 cm by 30 cm. If the wood is 1 cm thick, how many cm³ of wood is used in it?

What will happen to the volume of the cube, if its edge is tripled?

What will happen to the volume of the cube, if its edge is reduced to one-fourth?

When a die is thrown, list the outcome of an event of getting a number not greater than 5.

When a die is thrown, list the outcome of an event of getting not a prime number.

Show that (3x + 7)² − 84x = (3x − 7)²

Show that (9p - 5q)² + 180pq = (9p + 5q)²

Show that `(4/3 m - 3/4 n)^2 + 2mn = 16/9 m^2 + 9/16 n^2`

Show that `(4pq + 3q)^2 - (4pq - 3q)^2 = 48pq^2`

Show that (a - b)(a + b) + (b - c) (b + c) + (c - a) (c + a) = 0

Simplify the following using the formula: (a − b)(a + b) = a² − b²: (82)² − (18)²

Simplify the following using the formula: (a − b)(a + b) = a² − b²: (467)² − (33)²