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

In the figure of question 2, if E is the mid-point of median AD, then

prove that:

Area (ΔABE) = `1/4` Area (ΔABC).

The base BC of triangle ABC is divided at D so that BD = `1/2`DC.
Prove that area of ΔABD = `1/3` of the area of ΔABC.

In the following figure, OAB is a triangle and AB || DC.

If the area of ∆ CAD = 140 cm² and the area of ∆ ODC = 172 cm²,
find : (i) the area of ∆ DBC
(ii) the area of ∆ OAC
(iii) the area of ∆ ODB.

Use the table given below to find:
(a) The actual class limits of the fourth class.
(b) The class boundaries of the sixth class.
(c) The class mark of the third class.
(d) The upper and lower limits of the fifth class.
(e) The size of the third class.

The base of an isosceles triangle is 24 cm and its area is 192 sq. cm. Find its perimeter.

Four identical cubes are joined end to end to form a cuboid. If the total surface area of the resulting cuboid as 648 m²; find the length of the edge of each cube. Also, find the ratio between the surface area of the resulting cuboid and the surface area of a cube.

The volume of a cube is 729 cm³. Find its total surface area.

The square on the diagonal of a cube has an area of 1875 sq. cm. Calculate:
(i) The side of the cube.
(ii) The total surface area of the cube.

The edges of three cubes of metal are 3 cm, 4 cm, and 5 cm. They are melted and formed into a single cube. Find the edge of the new cube. 

Three cubes, whose edges are x cm, 8 cm, and 10 cm respectively, are melted and recast into a single cube of edge 12 cm. Find 'x'.

Three equal cubes are placed adjacently in a row. Find the ratio of the total surfaced area of the resulting cuboid to that of the sum of the total surface areas of the three cubes.

A square plate of side 'x' cm is 8 mm thick. If its volume is 2880 cm³; find the value of x.

Each face of a cube has a perimeter equal to 32 cm. Find its surface area and its volume.

The internal length, breadth, and height of a box are 30 cm, 24 cm, and 15 cm. Find the largest number of cubes which can be placed inside this box if the edge of each cube is
(i) 3 cm (ii) 4 cm (iii) 5 cm

When the length of each side of a cube is increased by 3 cm, its volume is increased by 2457 cm³. Find its side. How much will its volume decrease, if the length of each side of it is reduced by 20%?

The dimensions of a solid metallic cuboid are 72 cm × 30 cm × 75 cm. It is melted and recast into identical solid metal cubes with each edge 6 cm. Find the number of cubes formed.

Also, find the cost of polishing the surfaces of all the cubes formed at the rate Rs. 150 per sq. m.

The dimensions of a rectangular box are in the ratio 4: 2 : 3. The difference between the cost of covering it with paper at Rs. 12 per m² and with paper at the rate of 13.50 per m² is Rs. 1,248. Find the dimensions of the box. 

State for any acute angle θ whether sin θ increases or decreases as θ increases

Solve the following equation for A, if sin 3 A = `sqrt3 /2`

Calculate the value of A, if (sin A - 1) (2 cos A - 1) = 0