△ABC ∼ △DEF. If the areas of △ABC and △DEF are 100 cm² and 81 cm², respectively and the altitude of △DEF is 6.3 cm, then the corresponding altitude of △ABC is:

Find the area of the triangle whose sides are 5 cm, 12 cm and 13 cm.

A solid metallic sphere of radius 15 cm is melted and recast into spherical balls of radius 3 cm each. What is the ratio of the surface area of the original sphere and the sum of the surface areas of all the balls?

The perimeter of a semi-circle is 25.7 cm. What is its diameter (in cm)? (π = 3.14)

A prism with a right triangular base is 25 cm high. If the shorter sides of the triangle are in the ratio of 1 : 2 and the volume of the prism is 100 cm³ , what is the length of the longest side of the triangle?

In a circle with centre O, a diameter AB is produced to a point P lying outside the circle and PT is a tangent to the circle at the point C on it. If ∠BPT = 36°, then what is the measure of ∠BCP?

A hemispherical tank full of water is emptied by a pipe at the rate of 7.7 litres per second. How much time (in hours) will it take to empty part of the tank, if the internal radius of the tank is 10.5 m?

The circumference of the base of a right circular cone is 44 cm and its height is 24 cm. The curved surface area (in cm²) of the cone is: (Taken π=22/7)