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Find the volume of a sphere whose surface area is 154 cm². (Assume π = 22/7)

Given Surface area of sphere =154 cm2 Find out We have to find out the volume of the sphere Solution Let us say that the radius of a... View Article

Find the radius of a sphere whose surface area is 154 cm². (Assume π = 22/7)

Given The surface area of sphere is 154 cm² Find out We have to find out the radius of the sphere Solution Let the radius of the sphere be... View Article

Find the square roots of 100 and 169 by the method of repeated subtraction.

Solution For 100 100 – 1 = 99 [1] 99 – 3 = 96 [2] 96 – 5 = 91 [3] 91 – 7 = 84 [4] 84 – 9 = 75 [5] 75 – 11 = 64 [6] 64 – 13 = 51 [7] 51... View Article

A circle is a plane figure. Write True or False. Give reason for your answer

Write True or False: A circle is a plane figure. True. A circle is a 2d figure and it can be drawn on a plane. A circle is also termed... View Article

Find the 31st term of an A.P. whose 11th term is 38 and the 16th term is 73.

Given that, 11th term, a11 = 38 16th term, a16 = 73 Find out We have to find out the 31st term We know that,... View Article

Consider the following parallelograms. Find the values of the unknown x, y, z

Solution: (i) y = 100° {opposite angles of a parallelogram} x + 100° = 180° {Adjacent angles of a parallelogram} ⇒ x =... View Article

Solve 2x + 3y = 11 and 2x – 4y = – 24 and hence find the value of ‘m’ for which y = mx + 3.

2x + 3y = 11…………………………..(I) 2x – 4y =... View Article

Why will a sheet of paper fall slower than one that is crumpled into a ball?

A sheet of paper falls slower than the crumpled ball. A sheet of paper has a larger surface area when compared to a crumpled paper ball. A... View Article

If the moon attracts the earth, why does the earth not move towards the moon?

As per the universal law of gravitation and Newton’s third law, we all know that the force of attraction between two objects is the same,... View Article

Find the square of the following numbers. i) 32 ii) 35 iii) 86 iv) 93 v) 71 vi) 46

Solution (i) 32 (32)2 can be expressed as = (30 + 2)2 [From the identity, (a + b)2 = a2 + b2 + 2ab] =(30)2 + (2)2 + 2 × 30 × 2 = 900 + 4 +... View Article

Find the volume of a sphere whose radius is (i) 7 cm (ii) 0.63 m (Assume π = 22/7)

(i) Radius of sphere, r = 7 cm We know that Volume of sphere = (4/3) πr3 = (4/3)×(22/7)×73 = 4312/3 Hence, the volume... View Article

In a triangle ABC, E is the mid-point of median AD. Show that ar(BED) = 1/4 ar(ABC) .

ar(BED) = (1/2)×BD×DE Thus, E is the mid-point of AD, AE = DE Thus, AD is the median on side BC of triangle ABC,... View Article

For what value of n, are the nth terms of two APs 63, 65, 67, and 3, 10, 17, … equal?

Given data Two APs as; 63, 65, 67,… and 3, 10, 17,… Find out We need to find the value of n, for which nth term for both the given AP's are... View Article

If 17th term of an A.P. exceeds its 10th term by 7. Find the common difference.

Given that 17th term of an A.P. exceeds its 10th term by 7 Find out We need to find out the common difference Solution We know that for an A.P... View Article

In Fig. PQR = 100°, where P, Q and R are points on a circle with centre O. Find OPR.

Given ∠PQR=100°To find: ∠OPR=? SolutionReflex ∠POR=2∠PQR ——–[ The angle subtended by an arc at... View Article

In the above figure both RISK and CLUE are parallelograms. Find the value of x.

∠K + ∠R = 180° {adjacent angles of a parallelogram are supplementary} ⇒ 120° + ∠R = 180° ⇒ ∠R =... View Article

If the areas of two similar triangles are equal, prove that they are congruent.

Given: ΔABC and ΔPQR are two similar triangles and equal in area. ar(ΔABC) = ar(ΔPQR) To prove: ΔABC and ΔPQR are congruent. Proof: Similar... View Article

Find the height of a cuboid whose base area is 180 cm² and volume is 900 cm3?

Given the base area of the cuboid is 180 cm2 Th volume of cuboid is 900 cm3 Find out We have to find out the height of a... View Article

S and T are point on sides PR and QR of ΔPQR such that ∠P = ∠RTS. Show that ΔRPQ ~ ΔRTS.

Given S and T are point on sides PR and QR of ΔPQR And ∠P = ∠RTS. To Prove ΔRPQ ~ ΔRTS Proof In ΔRPQ and... View Article

Find the relation between x and y if the points (x, y) , (1, 2) and (7, 0) are collinear.

If given points are collinear then area of triangle formed by them must be zero. Let (x, y), (1, 2) and (7, 0) are vertices of a triangle, Area... View Article