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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

The diameters of front and rear wheels of a tractor are 80 cm and 2 m respectively. Find the number of revolutions that rear wheel will make in covering a distance in which the front wheel makes 1400 revolutions.

Given Diameter of front wheels = d1 = 80 cm Diameter of rear wheels = d2 = 2 m = 200 cm Number of revolutions made by the front... View Article

The area of a circular playground is 22176 m². Find the cost of fencing this ground at the rate of Rs 50 per metre.

Given Area of the circular playground = 22176 m2 Cost of fencing 1 meter of ground = Rs 50 Find out We have to determine the the... View Article

In Figure AB is a diameter of the circle, AC = 6 cm and BC = 8 cm. Find the area of the shaded region (Use π = 3.14).

Solution: According to the given details AC = 6cm BC = 8 cm A triangle in a semi-circle with hypotenuse as diameter is right... View Article

Find the area of the flower bed (with semi-circular ends) shown in Figure.

Solution: According to the given figure, Length of the rectangular portion AFDC of the flower bed is 38 cm Breadthof the... View Article

A cow is tied with a rope of length 14 m at the corner of a rectangular field of dimensions 20m × 16m. Find the area of the field in which the cow can graze.

Given Length of field = 20 m Breadth of the field = 16 m Let length of rope = 14 m Find out We have to determine the number of revolutions... View Article

The wheel of a motor cycle is of radius 35 cm. How many revolutions per minute must the wheel make so as to keep a speed of 66 km/h?

Given Radius of wheel = r = 35 cm Speed of the wheel = 66 km/hr Find out We have to determine the number of revolutions per minute Solution We... View Article

Find the area of a sector of a circle of radius 28 cm and central angle 45°.

Given Radius of circle = 28 cm Angle subtended at the center = 45° Find out We have to determine the area of the sector Solution Radius of... View Article

In Figure a square of diagonal 8 cm is inscribed in a circle. Find the area of the shaded region.

Solution: Let us assume the side of square to be S ∴ Diameter of a circle = Diagonal of the square = 8 cm From right... View Article

Find the radius of a circle whose circumference is equal to the sum of the circumferences of two circles of radii 15 cm and 18 cm.

Given Radius of first circle = r1 = 15 cm Radius of second circle = r2 = 18 cm Find out We have to determine the radius of a circle... View Article

In covering a distance s metres, a circular wheel of radius r metres makes s/2πr revolutions. Is this statement true? Why?

The given statement is True Solution The distance travelled by a circular wheel of radius r m in one revolution is equal to the... View Article

Is it true that the distance travelled by a circular wheel of diameter d cm in one revolution is 2 d cm? Why?

The given statement is False Solution Distance travelled by a circular wheel of radius r in one revolution equals the circumference of the... View Article