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The total surface area of a cube is 96 cm². The volume of the cube is: (A) 8 cm³ (B) 512 cm³ (C) 64 cm³ (D) 27 cm³

The correct answer is (C) 64 cm3 Explanation The surface area of a cube is 96 cm2 Let the length of the cube is a cm. Thus, 6 ×... View Article

The radius of a sphere is 2r, then its volume will be

The correct answer is (D) (32πr3)/3 Explanation The radius of a sphere is 2r. The volume of the given sphere = × π ×... View Article

A rectangular plot is given for constructing a house, having a measurement of 40 m long and 15 m in the front. According to the laws, a minimum of 3 m, wide space should be left in the front and back each and 2 m wide space on each of other sides. Find the largest area where house can be constructed.

Given Rectangular plot with length = 40cm and breadth =15cm 3m wide space is left in the front and back each and 2 m wide space on each of... View Article

The area of a trapezium is 475 cm² and the height is 19 cm. Find the lengths of its two parallel sides if one side is 4 cm greater than the other.

Given The area of a trapezium is 475 cm2 The height of the trapezium is 19 cm Length of parallel side is 4cm greater than the... View Article

The perimeter of a triangle is 50 cm. One side of a triangle is 4 cm longer than the smaller side and the third side is 6 cm less than twice the smaller side. Find the area of the triangle.

Given Perimeter = 50 cm One side of a triangle is 4 cm longer than the smaller side and the third side is 6 cm less than twice the smaller... View Article

How much paper of each shade is needed to make a kite given in figure in which ABCD is a square with diagonal 44 cm.

Solution According to the given diagram AC = BD = 44cm AO = 44/2 = 22cm BO = 44/2 = 22cm From ΔAOB, AB2 = AO2 + BO2... View Article

Find the area of a parallelogram given in figure Also find the length of the altitude from vertex A on the side DC.

Given According to the given details a = 12, b = 17, c = 25 Find out We have to determine the length of the altitude from vertex A on... View Article

From a point in the interior of an equilateral triangle, perpendiculars are drawn on the three sides. The lengths of the perpendiculars are 14 cm, 10 cm and 6 cm. Find the area of the triangle.

Given According to the given details The lengths of the perpendiculars are 14 cm, 10 cm and 6 cm. Find out We have to determine the area... View Article

The triangular side walls of a flyover have been used for advertisements. The sides of the walls are 13 m, 14 m and 15 m. The advertisements yield an earning of Rs 2000 per m² a year. A company hired one of its walls for 6 months. How much rent did it pay?

Given According to the given details The sides of the triangle are 13 m, 14 m and 15 m a = 13, b = 14, c = 15 Cost of laying grass in a... View Article

Find the cost of laying grass in a triangular field of sides 50 m, 65 m and 65 m at the rate of Rs 7 per m².

Given Sides of the triangular field are 50 m, 65 m and 65 m. a = 50, b = 65, c = 65 Cost of laying grass in a triangular field = Rs 7... View Article

The area of the equilateral triangle is 20√3 cm² whose each side is 8 cm. Write True or False and justify your answer.

The given statement is False Explanation Area of an equilateral triangle of side a = √3/4 a2 According to the given... View Article

The area of the isosceles triangle is 5/4 √11cm², if the perimeter is 11 cm and the base is 5 cm. Write True or False and justify your answer.

The given statement is True Explanation Area of triangle = √s(s-a)(s-b)(s-c) Perimeter = 11cm And base, a = 5 As the triangle is... View Article

The area of △ ABC is 8 cm² in which AB = AC = 4 cm and ∠A = 90º. Write True or False and justify your answer.

The given statement is True Explanation Area of triangle = × Base × Altitude Given that base= 4 cm height =6 cm =... View Article

The area of a triangle with base 4 cm and height 6 cm is 24 cm². Write True or False and justify your answer.

The given statement is False Explanation Area of triangle = × Base × Altitude Given that base= 4 cm height =6 cm =... View Article

The area of an equilateral triangle with side 2√3 cm is (A) 5.196 cm² (B) 0.866 cm² (C) 3.496 cm² (D) 1.732 cm²

The correct answer is (A) 5.196 cm2 An equilateral triangle has all three sides equal to each other. Due to this all the internal angles are of... View Article

The sides of a triangle are 56 cm, 60 cm and 52 cm long. Then the area of the triangle is (A) 1322 cm² (B) 1311 cm² (C) 1344 cm² (D) 1392 cm²

The correct answer is (C) 1344 cm2 Explanation We know that Area of triangle = √s(s-a)(s-b)(s-c) According to the given details... View Article

The perimeter of an equilateral triangle is 60 m. The area is (A) 10√3 m² (B) 15√3 m² (C) 20√3 m² (D) 100√3 m²

The correct answer is (D) 100√3 m2 Explanation We know that area of an equilateral triangle of side a = √3/4 a2 According to... View Article

An isosceles right triangle has area 8 cm². The length of its hypotenuse is (A) √32 cm (B) √16 cm (C) √48 cm (D) √24 cm

The correct answer is (A) √32 cm Explanation Let us assume height of triangle to be = h Given that the triangle is isosceles, Let... View Article

Construct each of the following and give justification: A triangle PQR given that QR = 3cm, ∠ PQR = 45° and QP – PR = 2 cm.

Solution According to the given details We have to construct a triangle PQR such that QR = 3cm, ∠ PQR = 45° and QP – PR... View Article

Construct each of the following and give justification: A triangle if its perimeter is 10.4 cm and two angles are 45° and 120°.

Solution According to the given details We have to construct a triangle if its perimeter is 10.4 cm and two angles are 45° and... View Article