(English Medium) ICSE Class 9 - CISCE Question Bank Solutions

If the bisector of an angle of a triangle bisects the opposite side, prove that the triangle is isosceles.

The length, breadth, and height of a rectangular solid are in the ratio 6 : 4 :3. If the total surface area is 1728 cm². Find its dimensions.

The length and breadth of a cuboid are 20 cm and 15 cm respectively. If its volume is 2400 cm³, find its height.

Find the volume of a cuboid whose diagonal is `3sqrt(29)"cm"` when its length, breadth and height are in the ratio 2 : 3 : 4.

The total surface area of a cuboid is 46m². If its height is 1m and breadth 3m, find its length and volume.

The length breadth and height of a cuboid are in the ratio of 3 : 3 : 4. Find its volume in m³ if its diagonal is `5sqrt(34)"cm"`.

A square plate of side 'x' cm is 4 mm thick. If its volume is 1440 cm³; find the value of 'x'.

A room is 22m long, 15m broad and 6m high. Find the area of its four walls and the cost of painting including doors and windows at the rate of Rs.12per m².

Three equal cubes of sides 5cm each are placed to form a cuboid. Find the volume and the total surface area of the cuboid.

A closed box is made of wood 5 mm thick. The external length, breadth and height of the box are 21 cm, 13 cm and 11 cm respectively. Find the volume of the wood used in making the box.

A room is 5m long, 2m broad and 4m high. Calculate the number of persons it can accommodate if each person needs 0.16m³ of air.

375 persons can be accommodated in a room whose dimensions are in the ratio of  6 : 4 : 1. Calculate the area of the four walls of the room if the each person consumes 64m³ of air.

Find the volume of wood used in making a closed box 22 cm by 18 cm by 14 cm, using a 1 cm thick wood. Also, find the cost of wood required to make the box at the rate of Rs. 5 per cm³ How many cubes of side 2 cm can be placed in the box?

The length of a cold storage is double its breadth. Its height is 3m. The area of its four walls including doors is 108m². Find its volume.

A metallic sheet is of the rectangular shape with dimensions 48cm x 36cm. From each one of its corners, a square of 8cm is cutoff. An open box is made of the remaining sheet. Find the volume of the box.

Express the equation 3x + 5y + 15 = 0 in the form such that:
a. x is subject to the formula
b. y is dependent variable and x is independent variable.

Is zero a rational number? Can it be written in the form `P/q`, where p and q are integers and q ≠ 0?

Arrange `-5/9, 7/12, -2/3 and 11/18` in ascending order of their magnitudes.
Also, find the difference between the largest and smallest of these rational numbers. Express this difference as a decimal fraction correct to one decimal place.

Arrange `5/8, -3/16, -1/4 and 17/32` in descending order of their magnitudes.
Also, find the sum of the lowest and largest of these fractions. Express the result obtained as a decimal fraction correct to two decimal places.

Without doing any actual division, find which of the following rational numbers have terminating decimal representation:

`7/16`