Surface Area & Volumes - Olympiad Level MCQ, Class 10 Mathematics - Class 10 MCQ

A river 3 m deep and 60 m wide is flowing at the rate of 2.4 km/h. The amount of water running into the sea per minute is:

If a solid right circular cylinder is made of iron is heated to increase its radius and height by 1 % each, then the volume of the solid is increased by :

If the right circular cone is separated into three solids of volumes V₁, V₂ and V₃ by two planes which are parallel to the base and trisects the altitude, then V₁ : V₂ : V₃ is :

Water flows at the rate of 10 m per minute from a cylindrical pipe 5 mm in diameter. A conical vessel whose diameter is 40 cm and depth 24 cm is filled. The time taken to fill the conical vessel is :

A cylinder circumscribes a sphere. The ratio of their volumes is:

If from a circular sheet of paper of radius 15 cm, a sector of 144° is removed and the remaining is used to make a conical surface, then the angle at the vertex will be :

A right circular cone of radius 4 cm and slant height 5 cm is curved out from a cylindrical piece of wood of same radius and height 5 cm. The surface area of the remaining wood is :

If h, s, V be the height, curved surface area and volume of a cone respectively, then (3πVh³ + 9V²– s²h²)is equal to :

If a cone is cut into two parts by a horizontal plane passing through the mid point of its axis, the ratio of the volumes of the upper part and the frustum is :

A cone, a hemisphere and a cylinder stand on equal bases of radius R and have equal heights H. Their whole surfaces are in the ratio:

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

A cylinder is circumscribed about a hemisphere and a cone is inscribed in the cylinder so as to have its vertex at the centre of one end and the other end as its base. The volumes of the cylinder, hemisphere and the cone are respectively in the ratio of:

A hollow sphere of outer diameter 24 cm is cut into two equal hemisphere. The total surface area of one of the hemisphere is 10054/7 cm². Each one of the hemisphere is filled with water. What is the volume of water that can be filled in each of the hemisphere?

A big cube of side 8 cm is formed by rearranging together 64 small but identical cubes each of side 2 cm. Further, if the corner cubes in the topmost layer of the big cube are removed, what is the change in total surface area of the big cube?

A large solid sphere of diameter 15 m is melted and recast into several small spheres of diameter 3 m. What is the percentage increase in the surface area of the smaller spheres over that of the large sphere?

A cone is made of a sector with a radius of 14 cm and an angle of 60°. What is total surface area of the cone?

If a cube of maximum possible volume is cut off from a solid sphere of diameter d, then the volume of the remaining (waste) material of the sphere would be equal to :

A piece of paper is in the form of a right angle triangle in which the ratio of base and perpendicular is 3 : 4 and hypotenuse is 20 cm. What is the volume of the biggest cone that can be formed by taking right angle vertex of the paper as the vertex of the cone?

In a particular country the value of diamond is directly proportional to the surface area (exposed) of the diamond.Four thieves steel a cubical diamond piece and then divide equally in four parts. What is the maximum percentage increase in the value of diamond after cutting it?

In a bullet the gun powder is to be filled up inside the metallic enclosure. The metallic enclosure is made up of a cylindrical base and conical top with the base of radius 5 cm. The ratio of height of cylinder and cone is 3 : 2. A cylindrical hole is drilled through the metal solid with height two-third the height of metal solid. What should be the radius of the hole, so that the volume of the hole (in which gun powder is to be filled up) is one-third the volume of metal solid after drilling?

A cubical cake is cut into several smaller cubes by dividing each edge in 7 equal parts. The cake is cut from the top along the two diagonals forming four prisms. Some of them get cut and rest remained in the cubical shape. A complete cubical (smaller) cake was given to adults and the cut off part of a smaller cake is given to a child (which is not an adult). If all the cakes were given equally each piece to a person, total how many people could get the cake?

In a factory there are two identical solid blocks of iron. When the first block is melted and recast into spheres of equal radii 'r', then 14 cc of iron was left, but when the second block was melted and recast into sphere each of equal radii '2r', then 36 cc of iron was left. The volumes of the solid blocks and all the spheres are in integers. What is the volume (in cm3) of each of the larger sphere of radius '2r'?