Archives

Shanti Sweets Stall was placing an order for making cardboard boxes for packing their sweets. Two sizes of boxes were required. The bigger of dimensions 25 cm×20cm×5cm and the smaller of dimension 15cm×12cm×5cm. For all the overlaps, 5% of the total surface area is required extra. If the cost of the cardboard is Rs. 4 for 1000 cm², find the cost of cardboard required for supplying 250 boxes of each kind.

Given The bigger of dimensions 25 cm×20cm×5cm and the smaller of dimension 15cm×12cm×5cm The cost of the cardboard... View Article

Mrs.Kaushik has a square plot with the measurement as shown in the figure. She wants to construct a house in the middle of the plot. A garden is developed around the house. Find the total cost of developing a garden around the house at the rate of Rs. 55 per m²

Given, Side of a square = 25 m Formula Area of square plot = square of a side = (side)2 = (25)2 = 625 Therefore, the area of a... View Article

A suitcase with measures 80 cm x 48 cm x 24 cm is to be covered with a tarpaulin cloth. How many meters of tarpaulin of width 96 cm is required to cover 100 such suitcases?

Solution: Given Length of suitcase box (l)= 80 cm, Breadth of suitcase box (b) = 48 cm Height of cuboidal box (h) = 24 cm Find out We have... View Article

The diagonal of a quadrilateral shaped field is 24 m and the perpendiculars dropped on it from the remaining opposite vertices are 8 m and 13 m. Find the area of the field.

Let us assume h1 = 13 m, h2 = 8 m AC = 24 m Area of quadrilateral ABCD = Area of triangle ABC + Area of triangle ADC =... View Article

A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarized it in the table given below. Find the mode of the data:

Number of cars Frequency 0-10 7 10-20 14 20-30 13 30-40 12 40-50 20 50-60 11 60-70 15 70-80 8 Solution Modal class = 30... View Article

The radii of two circles are 19 cm and 9 cm respectively. Find the radius of the circle which has a circumference equal to the sum of the circumferences of the two circles.

Given The radii of the two circles are 19 cm and 9 cm respectively Find out We have to find out the radius of the circle which has a... View Article

What is the magnitude of the gravitational force between the earth and a 1 kg object on its surface? (Mass of the earth is 6 × 1024 kg and radius of the earth is 6.4 × 106m.)

Given Mass of earth m1 =6 × 1024 kg Mass of the object m2 = 1 kg The radius of the earth =6.4 × 106 m Universal... View Article

The lateral surface area of a hollow cylinder is 4224cm². It is cut along its height and formed a rectangular sheet of width 33 cm. Find the perimeter of rectangular sheet?

Given The lateral surface area of hollow cylinder = 4224 cm² Height of hollow cylinder, h = 33 cm Find out We have to find out the... View Article

Three girls Reshma, Salma and Mandip are playing a game by standing on a circle of radius 5m drawn in a park. Reshma throws a ball to Salma, Salma to Mandip, Mandip to Reshma. If the distance between Reshma and Salma and between Salma and Mandip is 6m each, what is the distance between Reshma and Mandip?

Solution Given Let us assume the positions of Reshma, Salma and Mandip be represented as A, B and C respectively. From the question, we know... View Article

A company packages its milk powder in cylindrical container whose base has a diameter of 14 cm and height 20 cm. Company places a label around the surface of the container (as shown in figure) . If the label is placed 2 cm from top and bottom, what is the area of the label?

Given Diameter of cylindrical container (d) = 14 cm Radius of cylindrical container (r) = d / 2 = 14 / 2 = 7 cm Height of cylindrical... View Article

The side AB of a parallelogram ABCD is produced to any point P. A line through A and parallel to CP meets CB produced at Q and then parallelogram PBQR is completed (see Fig.) . Show that ar(ABCD) = ar(PBQR) . [Hint : Join AC and PQ. Now compare ar(ACQ) and ar(APQ) .]

Solution AC and PQ are joined. Ar(ΔACQ) = ar(ΔAPQ)(On the same base AQ and between the same parallel lines AQ and CP)... View Article

The runs scored by two teams A and B on the first 60 balls in a cricket match are given below: Represent the data of both the teams on the same graph by frequency polygons. [Hint: First make the class intervals continuous.]

Solution The data given in the question is represented in a discontinuous class interval. In order to make it in the continuous class interval,... View Article

A right triangle whose sides are 3 cm and 4 cm (other than hypotenuse) is made to revolve about its hypotenuse. Find the volume and surface area of the double cone so formed. (Choose value of π as found appropriate)

Given After revolving the triangle about its hypotenuse, we get two cones having slant height as 3 cm and 4 cm each. Hypotenuse of triangle (CD)... View Article

A school has 8 periods a day each of 45 minutes duration. How long would each period be, if the school has 9 periods a day, assuming the number of school hours to be the same?

Solution Let the duration of each period be x. Here the number of periods and the duration of periods are inversly proportional 8/9 =... View Article

A chord of a circle of radius 15 cm subtends an angle of 60° at the centre. Find the areas of the corresponding minor and major segments of the circle. (Use π = 3.14 and √3 = 1.73)

Given Given, Radius = 15 cm θ = 60° Find out The areas of the corresponding minor and major segments of the circle. Solution... View Article

In Fig. ABC is a right triangle right angled at A. BCED, ACFG and ABMN are squares on the sides BC, CA and AB respectively. Line segment AX ^ DE meets BC at Y. Show that: (i) ΔMBC ≅ ΔABD (ii) ar(BYXD) = 2ar(MBC) (iii) ar(BYXD) = ar(ABMN) (iv) ΔFCB ≅ ΔACE (v) ar(CYXE) = 2ar(FCB) (vi) ar(CYXE) = ar(ACFG) (vii) ar(BCED) = ar(ABMN) + ar(ACFG)

Solution Given: ∆ABC, right angled at A. BCED,ACFG,ABMN are squares at Y. i) To prove: ∆MBC ≅∆ABD Proof: In ∆MBC and ∆ABD MB=AB... View Article

From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Determine the height of the tower.

Let us assume that AB be the building of height 7 m EC be the height of the tower. A is the point from where elevation of tower is 60° and... View Article

An umbrella has 8 ribs which are equally spaced (see Fig.) . Assuming umbrella to be a flat circle of radius 45 cm, find the area between the two consecutive ribs of the umbrella.

Total ribs in umbrella=8 The radius of the umbrella is =45cm The area between the two consecutive ribs=1/8π*r2 So, the area of the circle (A)... View Article

Tick the correct solution in the following: Area of a sector of angle p (in degrees) of a circle with radius R is (A) p/180 × 2πR (B) p/180 × π R2 (C) p/360 × 2πR (D) p/720 × 2πR2

Option (D) p/720 × 2πR2 Solution The area of a sector = (θ/360°)×πr2 Given, θ = p So, area of sector =... View Article

Twenty-seven solid iron spheres, each of radius r and surface area S are melted to form a sphere with surface area S’. Find the (i) radius r’ of the new sphere, (ii) ratio of Sand S’.

We know that The volume of the solid sphere = (4/3)πr3 Hence, the volume of twenty-seven solid sphere = 27×(4/3)πr3 = 36... View Article