English Medium Class 10 - CBSE Question Bank Solutions for Mathematics

A bucket has top and bottom diameter of 40 cm and 20 cm respectively. Find the volume of the bucket if its depth is 12 cm. Also, find the cost of tin sheet used for making the bucket at the rate of Rs. 1.20 per dm² . (Use π = 3.14)

A frustum of a right circular cone has a diameter of base 20 cm, of top 12 cm, and height 3 cm. Find the area of its whole surface and volume.

On which axis do the following points lie?

P(5, 0)

On which axis do the following points lie?

Q(0, -2)

On which axis do the following points lie?

R(−4,0)

On which axis do the following points lie?

S(0,5)

Let ABCD be a square of side 2a. Find the coordinates of the vertices of this square when A coincides with the origin and AB and AD are along OX and OY respectively.

The perimeters of the ends of a frustum of a right circular cone are 44 cm and 33 cm. If the height of the frustum be 16 cm, find its volume, the slant surface and the total surface.

Let ABCD be a square of side 2a. Find the coordinates of the vertices of this square when The centre of the square is at the origin and coordinate axes are parallel to the sides AB and AD respectively.

The base PQ of two equilateral triangles PQR and PQR' with side 2a lies along y-axis such that the mid-point of PQ is at the origin. Find the coordinates of the vertices R and R' of the triangles.

If the radii of circular ends of a bucket 24cm high are 5cm and 15cm. find surface area of
bucket?

Find the distance between the following pair of points:

(a, 0) and (0, b)

The radii of the circular bases of a frustum of a right circular cone are 12 cm and 3 cm and the height is 12 cm. Find the total surface area and the volume of the frustum.

A tent consists of a frustum of a cone capped by a cone. If the radii of the ends of the frustum be 13 m and 7 m , the height of the frustum be 8 m and the slant height of the conical cap be 12 m, find the canvas required for the tent. (Take : π = 22/7)

A bucket made of aluminum sheet is of height 20cm and its upper and lower ends are of radius 25cm an 10cm, find cost of making bucket if the aluminum sheet costs Rs 70 per
100 cm²

Radii of circular ends of a solid frustum off a cone re 33cm and 27cm and its slant height are 10cm. find its total surface area?

A milk container is made of metal sheet in the shape of frustum of a cone whose volume is 10459 `3/7` cm³. The radii of its lower and upper circular ends are 8cm and 20cm. find the cost of metal sheet used in making container at rate of  Rs 1.4  per cm²?

Two vertices of an isosceles triangle are (2, 0) and (2, 5). Find the third vertex if the length of the equal sides is 3.

Which point on the x-axis is equidistant from (5, 9) and (−4, 6)?

Prove that the points (−2, 5), (0, 1) and (2, −3)  are collinear.