Class 10 Mathematics • Sample Paper Set 6

The total surface area of a solid hemisphere of radius $r$ is:

A cylinder, a cone and a hemisphere are of equal base and have the same height. What is the ratio of their volumes?

If two solid hemispheres of same base radius $r$ are joined together along their bases, then curved surface area of this new solid is:

The number of solid spheres, each of diameter 6 cm that can be made by melting a solid metal cylinder of height 45 cm and diameter 4 cm is:

If the radius of the base of a right circular cylinder is halved, keeping the height the same, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is:

The volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is:

A solid piece of iron in the form of a cuboid of dimensions 49 cm $\times$ 33 cm $\times$ 24 cm, is moulded to form a solid sphere. The radius of the sphere is:

The radii of the ends of a frustum of a cone of height $h$ cm are $r_1$ cm and $r_2$ cm. The volume in cm$^3$ is:

A shuttle cock used for playing badminton has the shape of the combination of:

The slant height of a bucket is 26 cm. The diameter of upper and lower ends are 36 cm and 16 cm. The height of the bucket is:

A metallic spherical shell of internal and external diameters 4 cm and 8 cm respectively is melted and recast into the form of a cone of base diameter 8 cm. The height of the cone is:

The surface area of a sphere is 616 cm$^2$. Its radius is:

A cylinder and a cone are of same base radius and of same height. The ratio of the volume of cylinder to that of the cone is:

Volume of a hollow cylinder with height $h$, outer radius $R$ and inner radius $r$ is:

If the surface area of a sphere is $144\pi$ cm$^2$, then its volume is:

A solid cylinder of radius $r$ and height $h$ is placed over other cylinder of same height and radius. The total surface area of the shape so formed is:

The number of cubes of side 2 cm which can be cut from a cube of side 6 cm is:

A pole 6 m high casts a shadow $2\sqrt{3}$ m long on the ground. The sun's elevation is:

Two cubes each of volume 64 cm$^3$ are joined end to end. Find the surface area of the resulting cuboid.

A sphere of maximum volume is cut out from a solid hemisphere of radius 6 cm. Find the volume of the cut out sphere.

A cone of height 24 cm and radius of base 6 cm is made up of modeling clay. A child reshapes it in the form of a sphere. Find the radius of the sphere.

The volume of a right circular cylinder with its height equal to the radius is $25\frac{1}{7}$ cm$^3$. Find the height of the cylinder.

A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.

A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top is 2.8 m, find the area of the canvas used for making the tent. Also, find the cost of the canvas of the tent at the rate of Rs 500 per m$^2$.

A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.

Water is flowing at the rate of 15 km/h through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44 m wide. In what time will the level of water in pond rise by 21 cm?

Three metallic solid spheres whose radii are 3 cm, 4 cm and 5 cm are melted and formed into a single solid sphere. Find the diameter of the sphere so formed.

A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of $\pi$.

A gulab jamun, contains sugar syrup up to about 30% of its volume. Find approximately how much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm.

A container, opened from the top and made up of a metal sheet, is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm, respectively. Find the cost of the milk which can completely fill the container, at the rate of Rs 20 per litre. Also find the cost of metal sheet used to make the container, if it costs Rs 8 per 100 cm$^2$.

Water in a canal, 6 m wide and 1.5 m deep, is flowing with a speed of 10 km/h. How much area will it irrigate in 30 minutes, if 8 cm of standing water is needed?

A bucket made of aluminum is of height 20 cm and has its upper and lower ends of radii 36 cm and 21 cm respectively. Find the volume of the bucket. Also find the cost of making the bucket if the cost of aluminum sheet is Rs 500 per 100 cm$^2$.

A cylindrical tub of radius 12 cm contains water to a depth of 20 cm. A spherical iron ball is dropped into the tub and thus the level of water is raised by 6.75 cm. What is the radius of the ball?

Case Study: Underground Water Tank
An underground water tank is in the shape of a cuboid of dimensions 2m x 2m x 1.5m. An overhead tank is in the shape of a cylinder of radius 50 cm and height 100 cm. Water from the underground tank is pumped to fill the overhead tank.

Case Study: Ice Cream Cone
An ice cream seller has a container in the shape of a right circular cylinder having diameter 12 cm and height 15 cm full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top.

Case Study: Medicine Capsule
A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm.