English Medium Class 9 - CBSE Question Bank Solutions

A cylindrical rod whose height is 8 times of its radius is melted and recast into spherical balls of same radius. The number of balls will be

If the ratio of volumes of two spheres is 1 : 8, then the ratio of their surface areas is 

If the surface area of a sphere is 144π m², then its volume (in m³) is 

If a solid sphere of radius 10 cm is moulded into 8 spherical solid balls of equal radius, then the surface area of each ball (in sq.cm) is

If a sphere is inscribed in a cube, then the ratio of the volume of the sphere to the volume of the cube is

If a solid sphere of radius r is melted and cast into the shape of a solid cone of height r, then the radius of the base of the cone is

A sphere is placed inside a right circular cylinder so as to touch the top, base and lateral surface of the cylinder. If the radius of the sphere is r, then the volume of the cylinder is 

The ratio between the volume of a sphere and volume of a circumscribing right circular cylinder is 

A cone and a hemisphere have equal bases and equal volumes the ratio of their heights is

A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is

In the given figure, the sides BC, CA and AB of a Δ ABC have been produced to D, E and F respectively. If ∠ACD = 105° and ∠EAF = 45°, find all the angles of the Δ ABC.

ABC is a triangle. The bisector of the exterior angle at B and the bisector of ∠C intersect each other at D. Prove that ∠D = \[\frac{1}{2}\] ∠A.

If the angles of a triangle are in the ratio 2 : 1 : 3, then find the measure of smallest angle.

In the given figure, if AB || DE and BD || FG such that ∠FGH = 125° and ∠B = 55°, find x and y.

In ΔABC, if ∠A = 100°, AD bisects ∠A and AD ⊥ BC. Then, ∠B =

In a ΔABC, if ∠A = 60°, ∠B = 80° and the bisectors of ∠B and ∠C meet at O, then ∠BOC =

Line segments AB and CD intersect at O such that AC || DB. If ∠CAB = 45° and ∠CDB = 55°, then ∠BOD =