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Metal spheres, each of radius 2 cm, are packed into a rectangular box of internal dimensions 16 cm × 8 cm × 8 cm. When 16 spheres are packed the box is filled with preservative liquid. Find the volume of this liquid. Give your answer to the nearest integer. [Use π = 3.14]

Given Radius of each sphere, r = 2 cm Number of spheres = 16 Dimensions of rectangular box = 16 cm × 8 cm × 8 cm Find out We... View Article

The volume of the largest right circular cone that can be fitted in a cube whose edge is 2r equals to the volume of a hemisphere of radius r. Write True or False and justify your answer in the following.

The given statement is True Explanation According to the given details Edge of the cube, l = 2r Then, the diameter of the cone = 2r... View Article

If the radius of a cylinder is doubled and its curved surface area is not changed, the height must be halved. Write True or False and justify your answer in the following.

The given statement is True Explanation Let us assume a right circular cylinder, with height as h and radius r. Then, the curved... View Article

In a right circular cone, height, radius and slant height do not always be sides of a right triangle. Write True or False and justify your answer in the following.

The given statement is True Explanation Let us assume a right circular cone, with height as h, slant height l and radius r. In a... View Article

If the radius of a right circular cone is halved and height is doubled, the volume will remain unchanged. Write True or False and justify your answer in the following.

The given statement is False Explanation Let us assume the original radius of the cone = r Let us assume the height of the cone = h. The... View Article

The volume of a sphere is equal to two-third of the volume of a cylinder whose height and diameter are equal to the diameter of the sphere. Write True or False and justify your answer in the following.

The given statement is True Explanation Let us assume the radius of the sphere = r. According to the given details height and... View Article

The total surface area of a cone whose radius is r/2 and slant height 2l is

The correct answer is (B) πr(l+(r/4)) Explanation The radius of a cone is r/2 and the slant height is 2L. Total surface area... View Article

In a cylinder, radius is doubled and height is halved, curved surface area will be (A) halved (B) doubled (C) same (D) four times

The correct answer is (C) the same Explanation Let us assume the radius of a cylinder = r unit Letus assume the height of a cylinder = h unit.... View Article

A cone is 8.4 cm high and the radius of its base is 2.1 cm. It is melted and recast into a sphere. The radius of the sphere is: (A) 4.2 cm (B) 2.1 cm (C) 2.4 cm (D) 1.6 cm

The correct answer is (B) 2.1 cm Explanation Height of cone, h = 8.4cm Radius of base, r = 2.1cm Thus volume of a cone = × π... View Article

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