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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

A cylindrical pencil sharpened at one edge is the combination of (A) a cone and a cylinder (B) frustum of a cone and a cylinder (C) a hemisphere and a cylinder (D) two cylinders.

The correct answer is (A) a cone and a cylinder Solution The Nib of a sharpened pencil is in the shape of the cone The rest of the part... View Article

On a square cardboard sheet of area 784 cm2, four congruent circular plates of maximum size are placed such that each circular plate touches the other two plates and each side of the square sheet is tangent to two circular plates. Find the area of the square sheet not covered by the circular plates.

Given Area of the square = 784 cm2 Find out We have to determine the area of the square sheet not covered by the circular plates. Solution... View Article

Four circular cardboard pieces of radii 7 cm are placed on a paper in such a way that each piece touches other two pieces. Find the area of the portion enclosed between these pieces.

Given Radius of each sector = 7 cm Find out We have to determine the area of the portion enclosed between these pieces. Solution The four... View Article

Find the area of the sector of a circle of radius 5 cm, if the corresponding arc length is 3.5 cm.

Given Radius of the circle = r = 5 cm Arc length of the sector = l = 3.5 cm Find out We have to determine the area of the sector of a circle... View Article

Three circles each of radius 3.5 cm are drawn in such a way that each of them touches the other two. Find the area enclosed between these circles.

Given Three circles each of radius 3.5 cm Find out We have to determine the area enclosed between these circles. Solution The three... View Article

In Figure ABCD is a trapezium with AB || DC, AB = 18 cm, DC = 32 cm and distance between AB and DC = 14 cm. If arcs of equal radii 7 cm with centres A, B, C and D have been drawn, then find the area of the shaded region of the figure.

Given AB = 18 cm, DC = 32 cm Distance between AB and DC = Height = 14 cm Radius of each arc = 7 cm Find out We have to determine the cost... View Article

A circular pond is 17.5 m is of diameter. It is surrounded by a 2 m wide path. Find the cost of constructing the path at the rate of Rs 25 per m2

Given Diameter of the circular pond = 17.5 m The circular pond is surrounded by a path of width 2 m. Cost of constructing the path per... View Article

Find the area of the segment of a circle of radius 12 cm whose corresponding sector has a central angle of 60° (Use π = 3.14).

Given Radius of the circle = r = 12 cm Central angle formed by the sector=60° Find out We have to determine the area of the segment of a... View Article

Sides of a triangular field are 15 m, 16 m and 17 m. With the three corners of the field a cow, a buffalo and a horse are tied separately with ropes of length 7 m each to graze in the field. Find the area of the field which cannot be grazed by the three animals.

Given Sides of the triangle are 15 m, 16 m, and 17 m. Length of the rope to which cow, horse and buffalo are tied=7cm Find out We have to... View Article