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Diameter of cylinder A is 7 cm and the height is 14 cm. Diameter of cylinder B is 14 cm and height is 7 cm. Without doing any calculations can you suggest whose volume is greater? Verify it by finding the volume of both the cylinders. Check whether the cylinder with greater volume also has greater surface area.

Solution Cylinder A: Radius of cylinder A = 7/2 cm Height of cylinder A = 14 cm Volume of cylinder A = ∏.r2h = 22/7 x 7/2 x 7/2 x 14... View Article

Length of the fence of a trapezium shaped field ABCD is 120 m. If BC = 48 m, CD = 17 m and AD = 40 m, find the area of this field. Side AB is perpendicular to the parallel sides AD and BC.

Given: BC = 48 m, CD = 17 m, AD = 40 m perimeter = 120 m ∵ Perimeter of trapezium ABCD = AB + BC + CD + DA 120 = AB + 48 + 17 + 40... View Article

Yamini and Fatima, two students of Class IX of a school, together contributed Rs. 100 towards the Prime Minister’s Relief Fund to help the earthquake victims. Write a linear equation which satisfies this data. (You may take their contributions as Rs. x and Rs. y.) Draw the graph of the same.

Let’s assume Yamini’s contribution as ₹ x and Fatima’s contribution as ₹ y. As they together contributed ₹ 100, so the... View Article

Three coins were tossed 30 times simultaneously. Each time the number of heads occurring was noted down as follows: 0 1 2 2 1 2 3 1 3 0 1 3 1 1 2 2 0 1 2 1 3 0 0 1 1 2 3 2 2 0 Prepare a frequency distribution table for the data given above.

The frequency distribution table for the data given in the question is tabulated below: Number of Heads Frequency 0 6 1 10 2 9 3 5... View Article

Let ABC be a right triangle in which AB = 6 cm, BC = 8 cm and ∠ B = 90°. BD is the perpendicular from B on AC. The circle through B, C, D is drawn. Construct the tangents from A to this circle. Give the justification of the construction

To construct a tangent from given conditions 1. Let us draw the line segment with base BC = 8cm 2. Estimate the angle 90° at point B,... View Article

A metal pipe is 77 cm long. The inner diameter of a cross section is 4 cm, the outer diameter being 4.4cm. (see fig.) . Find its (i) inner curved surface area, (ii) outer curved surface area (iii) total surface area (Assume π = 22/7)

Given Height of Cylindrical metal pipe (h) =77 cm The inner diameter of metal pipe (d)=4cm, The outer diameter of metal pipe... View Article

The slant height and base diameter of conical tomb are 25m and 14 m respectively. Find the cost of white-washing its curved surface at the rate of Rs. 210 per 100 m2. (Assume π = 22/7)

Given Slant height of conical tomb, l = 25m Base radius, r = diameter/2 = 14/2 m = 7m Find out We have to find the cost of white-washing its... View Article

The following table gives the life times of 400 neon lamps:(i) Represent the given information with the help of a histogram. (ii) How many lamps have a life time of more than 700 hours?

Life Time (in hours) Number of lamps 300 - 400 14 400 - 500 56 500 - 600 60 600 - 700 86 700 - 800 74 800 - 900 62 900 - 1000 48... View Article

In one fortnight of a given month, there was a rainfall of 10 cm in a river valley. If the area of the valley is 97280 km2, show that the total rainfall was approximately equivalent to the addition to the normal water of three rivers each 1072 km long, 75 m wide and 3 m deep.

Given The surface area of a river = [1072×(75/1000)] km Depth = (3/1000) km Solution The total volume of 3 rivers = 3×[(Surface area... View Article

A die is thrown twice. What is the probability that (i) 5 will not come up either time? (ii) 5 will come up at least once? [Hint : Throwing a die twice and throwing two dice simultaneously are treated as the same experiment]

Outcomes are: (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6) (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6) (3, 1), (3, 2), (3, 3), (3, 4),... View Article

The lengths of two parallel chords of a circle are 6 cm and 8 cm. If the smaller chord is at a distance 4 cm from the centre, what is the distance of the other chord from the centre?

Solution AB and CD are 2 parallel chords. Now, join OB and OD. Distance of smaller chord AB from the centre of the circle = 4 cm... View Article

In Fig., AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.

Given Radius of larger circle, R = 7 cm Radius of smaller circle, r = 7/2 cm Height of ΔBCA = OC = 7 cm Base of ΔBCA = AB = 14 cm... View Article

A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 years, she prefers to have a slide whose top is at a height of 1.5 m, and is inclined at an angle of 30° to the ground, whereas for elder children, she wants to have a steep slide at a height of 3m, and inclined at an angle of 60° to the ground. What should be the length of the slide in each case?

As per contractor’s plan, Let, ABC is the slide inclined at 30° with length AC and PQR is the slide inclined at 60° with length... View Article

Let A (4, 2) , B (6, 5) and C (1, 4) be the vertices of ∆ ABC. (i) The median from A meets BC at D. Find the coordinates of point D. (ii) Find the coordinates of the point P on AD such that AP : PD = 2 : 1. (iii) Find the coordinates of point Q and R on medians BE and CF respectively such that BQ : QE = 2:1 and CR : RF = 2 : 1. (iv) What do you observe? [Note : The point which is common to all the three medians is called the centroid and this point divides each median in the ratio 2 : 1.](v) If A (x1, y1) , B (x2, y2) and C (x3, y3) are the vertices of triangle ABC, find the coordinates of the centroid of the triangle.

(i) Coordinates of D can be calculated as follows: Coordinates of D = (ii) Coordinates of P can be calculated as follows: Coordinates of P =... View Article

A plastic box 1.5 m long, 1.25 m wide and 65 cm deep, is to be made. It is to be open at the top. Ignoring the thickness of the plastic sheet, determine: (i) The area of the sheet required for making the box. (ii) The cost of sheet for it, if a sheet measuring 1m2 costs Rs. 20.

Given Length of box (l) = 1.5 m Breadth of box (b) = 1.25 m Height of box (h) = 65 cm = 0.65 m The box is open at top Solution (i) The area... View Article

A small indoor greenhouse (herbarium) is made entirely of glass panes (including base) held together with tape. It is 30cm long, 25 cm wide and 25 cm high. (i) What is the area of the glass? (ii) How much of tape is needed for all the 12 edges?

Given Length of greenhouse (l) = 30 cm Breadth of greenhouse (b) = 25 cm Height of greenhouse (h) = 25 cm Find out We have to find the ... View Article

A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm, which is surmounted by another cylinder of height 60 cm and radius 8 cm. Find the mass of the pole, given that 1 cm3 of iron has approximately 8 g mass.

Given Height of large cylinder (H)= 220 cm Radius of large cylinder (R)= 24/2 = 12 cm Height of small cylinder (h)= 60 cm Radius of small... View Article

A fez, the cap used by the Turks, is shaped like the frustum of a cone (see Fig.) . If its radius on the open side is 10 cm, radius at the upper base is 4 cm and its slant height is 15 cm, find the area of material used for making it.

Given Slant height of frustum (l)= 15 cm Let radius of smaller circle end (r) = 4 cm Let radius of larger circle end (R) = 10 cm Find out We... View Article

The following distribution gives the daily income of 50 workers if a factory. Convert the distribution above to a less than type cumulative frequency distribution and draw its ogive.

Daily income in Rupees 100-120 120-140 140-160 160-180 180-200 Number of workers 12 14 8 6 10 Solution Let find the cumulative... View Article

The lengths of 40 leaves in a plant are measured correctly to the nearest millimeter, and the data obtained is represented as in the following table: Find the median length of leaves.

Length (in mm) Number of leaves 118-126 3 127-135 5 136-144 9 145-153 12 154-162 5 163-171 4 172-180 2 Solution: The data... View Article