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Two cones with same base radius 8 cm and height 15 cm are joined together along their bases. Find the surface area of the shape so formed.

Given Two cones same dimensions Radius of cone, r = 8 cm Height of cone h = 15 cm Find out We have to determine the surface area of the... View Article

From a solid cube of side 7 cm, a conical cavity of height 7 cm and radius 3 cm is hollowed out. Find the volume of the remaining solid.

Given Side of a cube = 7 cm Radius of cone, r = 3 cm Height of cone, h = 7 cm From the given cube a cone is hallowed out Find out We have... View Article

Two identical cubes each of volume 64 cm³ are joined together end to end. What is the surface area of the resulting cuboid?

Given Two identical cubes each of volume 64 cm3 are joined together Find out We have to determine the surface area of resulting cuboid... View Article

A cone of radius 8 cm and height 12 cm is divided into two parts by a plane through the mid-point of its axis parallel to its base. Find the ratio of the volumes of two parts.

Given Height of cone = 12 cm Radiuc of cone = 8cm The cone is divided into two parts by a plane through the mid-point of its axis parallel to... View Article

A bucket is in the form of a frustum of a cone and holds 28.490 litres of water. The radii of the top and bottom are 28 cm and 21 cm, respectively. Find the height of the bucket.

Given Volume of bucket = 28.490 L Radius of top, r1 = 28 cm Radius of bottom, r2 = 21 cm Find out We have to determine... View Article

How many shots each having diameter 3 cm can be made from a cuboidal lead solid of dimensions 9cm × 11cm × 12cm?

Given Diameter of spherical shot=3cm Cuboid dimensions Length, l = 9 cm Breadth, b = 11 cm Height, h = 12 cm These 3 cubes are melted to... View Article

Three metallic solid cubes whose edges are 3 cm, 4 cm and 5 cm are melted and formed into a single cube. Find the edge of the cube so formed.

Given Side of first cube, a1 = 3 cm Side of second cube, a2 = 4 cm Side of third cube, a3 = 5 cm These 3 cubes are melted to... View Article

A solid ball is exactly fitted inside the cubical box of side a. The volume of the ball is 4/3πa3. Write ‘True’ or ‘False’ and justify your answer

The given statement is False Solution According to the given data Let the radius of sphere = r When a solid ball is exactly fitted... View Article

A solid cone of radius r and height h is placed over a solid cylinder having same base radius and height as that of a cone. The total surface area of the combined solid is πr[√(r2 + h2 + 3r + 2h]. Write ‘True’ or ‘False’ and justify your answer

The given statement is False Solution According to the given data When a solid cone is placed over a solid cylinder of same base radius,... View Article

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 4πrh + 4πr2. Write ‘True’ or ‘False’ and justify your answer

The given statement is False Solution According to the given data When one cylinder is placed over another, the base of first cylinder... View Article

Two identical solid hemispheres of equal base radius r cm are stuck together along their bases. The total surface area of the combination is 6πr2. Write ‘True’ or ‘False’ and justify your answer

The given statement is False Solution When two hemispheres are joined together along their bases, a sphere of same base radius is formed.... View Article

A solid piece of iron in the form of a cuboid of dimensions 49cm × 33cm × 24cm, is moulded to form a solid sphere. The radius of the sphere is (A) 21cm (B) 23cm (C) 25cm (D) 19cm

The correct answer is (A) 21cm Given For given cuboid, Length, l = 49 cm Breadth, b = 33 cm Height, h = 24 cm The cone is moulded to... View Article

A metallic spherical shell of internal and external diameters 4 cm and 8 cm, respectively is melted and recast into the form a cone of base diameter 8cm. The height of the cone is (A) 12cm (B) 14cm (C) 15cm (D) 18cm

The correct answer is (B) 14cm Given Internal diameter, d1 = 4 cm External diameter, d2 = 8 cm Base diameter of cone = 8... View Article

A hollow cube of internal edge 22cm is filled with spherical marbles of diameter 0.5 cm and it is assumed that 1/8 space of the cube remains unfilled. Then the number of marbles that the cube can accommodate is (A) 142296 (B) 142396 (C) 142496 (D) 142596

The correct answer is (A) 142296 Given Edge of cube= 22cm Diameter of spherical marble = d=0.5cm Amount of space unfilled in the cube =... View Article

A cone is cut through a plane parallel to its base and then the cone that is formed on one side of that plane is removed. The new part that is left over on the other side of the plane is called (A) a frustum of a cone (B) cone (C) cylinder (D) sphere

The correct answer is (A) a frustum of a cone Solution When a cone is divided into two parts by a plane through any point on its axis... View Article

A shuttle cock used for playing badminton has the shape of the combination of (A) a cylinder and a sphere (B) a cylinder and a hemisphere (C) a sphere and a cone (D) frustum of a cone and a hemisphere

The correct answer is (D) frustum of a cone and a hemisphere Solution The cork of a shuttle is in the shape of a hemisphere The upper... View Article

The shape of a gilli, in the gilli-danda game (see Figure), is a combination of (A) two cylinders (B) a cone and a cylinder (C) two cones and a cylinder (D) two cylinders and a cone

The correct answer is(C) two cones and a cylinder Solution The left and right part of a gilli is in the shape of a cone The central part of... View Article

The shape of a glass (tumbler) (see figure) is usually in the form of (A) a cone (B) frustum of a cone (C) a cylinder (D) a sphere

The correct answer is (B) frustum of a cone Solution The shape of the glass is a frustum or specifically, an inverted frustum.... View Article

A plumbline (sahul) is the combination of (see Figure (A) a cone and a cylinder (B) a hemisphere and a cone (C) frustum of a cone and a cylinder (D) sphere and cylinder

The correct answer is (B) a hemisphere and a cone Solution The upper part of the plumbline is in the shape of a hemisphere The bottom part... View Article

A surahi is the combination of (A) a sphere and a cylinder (B) a hemisphere and a cylinder (C) two hemispheres (D) a cylinder and a cone.

The correct answer is (A) a sphere and a cylinder Solution The top part of surahi is in the shape of a cylinder The bottom part of... View Article