A sphere of diameter 12 cm, is dropped in a right circular cylindrical vessel, partly filled with water. If the sphere is completely submerged in water, the water level in the cylindrical vessel rises by 35 9 cm. Find the diameter of the cylindrical vessel.

In figure, a circle inscribed in triangle ABC touches its sides AB, BC and AC at points D, E and F respectively. If AB = 12 cm, BC=8 cm and AC=10 cm, then find the lengths of AD, BE and CF.

In figure, AP =2 cm, BQ = 3 cm and RC =4 cm, then find the perimeter of ΔABC

If AB =12 cm, BC = 16 cm and AB is perpendicular to BC then the radius of the circle passing through the points A,B and C is : 6 cm 8 cm 10 cm 12 cm

Find the volume and lateral surface area of the cuboid dimensions are length = 22 cm, breadth = 12 cm and height = 7.5 cm.

In the given figure ABC is a triangle and GHED is a rectangle B C = 12 cm, H E = 6 cm, F C = B F and altitude A F is 24 cm. The area of the rectangle is ______

In the given figure, a circle inscribed in a triangle ABC, touches the sides AB, BC and AC at points D, E and F respectively. If AB = 12 cm, Bc = 8 cm and AC = 10 cm, find the lengths fo AD, BE and CF.

In the figure, O is the centre of a circle such that diameter AB =13 cm and AC =12 cm. BC is joined. Find the area of the shaded region. (Take π = 3.14).

Hence, the image of the needle is 6.7 cm away from the mirror. Also, it is on the other side of the mirror.

Find the area of an equilateral triangle whose area is equal to the triangle of sides 12 cm, 8 cm and 16 cm.