Find the volume (in cm3) of a hemisphere of diameter 42 cm.

A spherical glass vessel has a cylindrical neck 7 cm long and 4 cm in diameter. The diameter of the spherical part is 21 cm. Find the quantity of water it can hold.

The diagonals are congruent in a _____.

In a right angled triangle ΔDEF, if the length of the hypotenuse EF is 12 cm, then the length of the median DX is

ABCD is a cyclic quadrilateral of which AB is the diameter. Diagonals AC and BD intersect at E. If ∠DBC = 35°, Then ∠AED measures

The length of one side of a rhombus is 41 cm and its area is 720 sq.cm. What is the sum of the lengths of its diagonals?

A solid right circular cone of radius 10 cm and height 8 cm is put inside a cylindrical vessel of radius 11 cm and height 9 cm. How much water in cubic cm will be required to fill the cylindrical vessel completely?

If the angles of a triangle are in the ratio of 2 : 5 : 8, then find the value of the smallest angle.

The height and the total surface area of a right circular cylinder are 4 cm and 8π sq.cm. respectively. The radius of the base of cylinder is

ΔABC is similar to ΔDEF. Length of AB is 18 cm and length of the corresponding side DE is 10 cm. What is the ratio of Perimeter of ΔABC : Perimeter of ΔDEF?

For the figure given below, find the value (in degrees) of 2∠A + ∠B.

A cone of height 12 cm and diameter 10 cm is mounted on a hemisphere of the same diameter. What is the volume of the solid thus formed?

At what point does the line 3x + y = -6 intercept the x-axis?

The area and the length of one of the diagonals of a rhombus is 54 cm2 and 9 cm respectively. Find the length of its other diagonal (in cm).

Δ DEF is right angled at E. If m∠F = 45°, then what is the value of 2 Sin F x Cot F?

The orthocentre of a triangle is the point where

The sum of the lengths of the edges of a cube is equal to half the perimeter of a square. If the numerical value of the volume pf the cube is equal to one-sixth of the numerical value of the area of the square, then the length of one side of the square is

ΔABC is similar to ΔDEF. Length of AB is 12 cm and length of the corresponding side DE is 8 cm. What is the ratio of Perimeter of ΔABC : Perimeter of ΔDEF?

What is the slope of the line parallel to the line passing through the points (6,­3) and (2,­1)?

An arc of 30° in one circle is double an arc in a second circle, the radius of which is three times the radius of the first. Then the angles subtended by the arc of the second circle at its centre is

Two circles touch each other externally. The distance between their centres is 7 cm. If the radius of one circle is 4 cm, then the radius of the other circle will be

ΔABC is right angled at B. BD is the altitude. AD is 8 cm and DC is 50 cm. What is the length of BD?

The co-ordinates of the centroid of a triangle ABC are (-1 , 4). What are the co-ordinates of vertex C if co-ordinates of A and B are (-3 , -1) and (3 , 5) respectively?

Find the total surface area (in cm²) of a right circular cone of diameter 14 cm and slant height 10 cm.

The length and breadth of a rectangular piece of a land are in a ratio 5:The owner spent Rs. 6000 for surrounding it from all sides at Rs.7.50 per metre. The difference between its length and breadth is

If the edge of a cube is increased by 2 cm, the volume will increase by 488 cub.cm. What then will be the length of each edge of the cube?

What is the diameter (in cm) of a sphere of surface area 6.16 sq cm?

The triangle in which the orthocenter, circumcentre, Incenter and the centroid coincide each other at a point is known as _____________.

The internal bisectors of ∠Q and ∠R of triangle PQR meet at O. If ∠P = 70°, then what is the measure of ∠QOR (in degrees)?

Length of the sides of a triangle are a, b, c respectively. If a2 + b2 + c2 = ab +bc + ca then the triangle is

What is the diameter (in cm) of a sphere of surface area 154 sq cm?

The total surface area of a hemisphere is 41.58 sq cm, find its radius.

If the edge of a cube is increased by 4 cm, the volume will increase by 988 . Then the original length of each edge of the cube is

AD is the Median of Δ ABC. If O is the centroid and AO = 10 cm then OD is

Find the volume (in cm3) of a cuboid of length, breadth and height of 8.5 cm, 6 cm and 7 cm respectively.

The measures of the four angles of a quadrilateral are in the ratio 1:2:4:What is the measure of the biggest angle?

What is the area (in sq cm) of a regular hexagon of side 14 cm?

In a rhombus _____.

The diameter of a sphere is twice the diameter of another sphere. The curved surface area of the first and the volume of the second are numerically equal. The numerical value of the radius of the first sphere is

What can be the maximum number of common tangent which can be drawn to two non-intersecting circles?

Slope of the line AB is 4/Co-ordinates of points A and B are (x , -5) and (2 , -3) respectively. What is the value of x?

The ratio between the vertical angle and a base angle of an isosceles triangle is 4:The value of any one base angle is

What is the area (in square units) of the figure enclosed by the graphs of the lines x = -4, x =2, y = -2 and y = 3?

Find the circumference (in cm) of a circle of radius 17.5 cm.

In what ratio does the point T(x,0) divide the segment joining the points S(-4,-1) and U(1,4)?

In ΔPQR, PQ = PR = 18 cm, AB and AC are parallel to lines PR and PQ respectively. If A is the mid-point of QR, then what is the perimeter (in cm) of quadrilateral ABPC?

The length of two parallel sides of a trapezium are 18 m and 24 m. If its height is 12 m, then what is the area (in sq.m) of the trapezium?

If ax - 4y = -6 has a slope of -3/What is the value of a?

If the circum radius of the equilateral triangle is 12 cm then what is the value of in radius (in cm) of the triangle?