CBSE Class 8 Mathematics Mensuration Worksheet Set C

CBSE Class 8 Mathematics Worksheet - Mensuration (1)

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Question. One side of a rectangular field is 15 m and one of its diagonals is 17 m. Find the area of the field.
Answer: 120 \(m^2\)

Question. A lawn is in the form of a rectangle having its sides in the ratio \(2 : 3\). the area of the lawn is \(\frac{1}{6}\) hectares. Find the length and breadth of the lawn.
Answer: 50 m.

Question. Find the cost of carpeting a room 13 m long and 9 m broad with a carpet 75 cm wide at the rate of Rs. 12.40 per square metre.
Answer: 1934.4

Question. If the diagonal of a rectangle is 17 cm long and its perimeter is 46 cm, find the area of the rectangle.
Answer: 120 \(cm^2\)

Question. The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 75 sq. cm. Find the length of the rectangle.
Answer: 20 cm

Question. In measuring the sides of a rectangle, one side is taken 5% in excess, and the other 4% in deficit. Find the error percent in the area calculated from these measurements.
Answer: 0.8%

Question. A rectangular grassy plot 110 m by 65 m has a gravel path 2.5 m wide all round it on the inside. Find the cost of greavelling the path at 80 paise per sq. metre.
Answer: 680

Question. The perimeters of two squares are 40 cm and 32 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares.
Answer: 24 cm

Question. A room 5 m 55 cm long and 3m 74 cm broad is to be paved with square tiles. Find the least number of square tiles required to cover the floor.
Answer: 176

Question. Find the area of a square, one of whose diagonals is 3.8 m long.
Answer: 7.22 \(m^2\)

Question. The diagonals of two squares are in the ratio of \(2 : 5\). Find the ratio of their areas.
Answer: \(4 : 5\)

Question. If each side of a square is increased by 25%, find the percentage change in its area.
Answer: 56.25%

Question. If the length of a certain rectangle is decreased by 4 cm and the width is increased by 3 cm, a square with the same area as the original rectangle would result. Find the perimeter of the original rectangle.
Answer: 50 cm

Question. A room is half as long again as it is broad. The cost of carpeting the room at Rs. 5 per sq. m is Rs. 270 and the cost of papering the four walls at Rs. 10 per \(m^2\) is Rs. 1720. If a door and 2 windows occupy 8 sq.m, find the dimensions of the room.
Answer: L = 9, B = 6, H = 6

Question. Find the area of a triangle whose sides measure 13 cm, 14 cm and 15 cm.
Answer: 84 \(cm^2\)

Question. Find the area of a right-angled triangle whose base is 12 cm and hypotenuse 13 cm.
Answer: 30 \(cm^2\)

Question. The base of a triangular field is three times its altitude. If the cost of cultivating the field at Rs. 24.68 per hectare be Rs. 333.18, find its base and height.
Answer: B = 900 m, H = 300 m.

Question. The altitude drawn to the base of an isosceles triangle is 8 cm and the perimeter is 32 cm. Find the area of the triangle.
Answer: 60 \(cm^2\)

Question. Find the length of the altitude of an equilateral triangle of side \(3\sqrt{3}\) cm.
Answer: 4.5 cm

Question. In two triangles, the ratio of the areas is \(4 : 3\) and the ratio of their heights is \(3 : 4\). Find the ratio of their bases.
Answer: \(16 : 9\)

Question. The base of a parallelogram is twice its height. If the area of the parallelogram is 72 sq. cm, find its height.
Answer: 6 cm

Question. Find the area of a rhombus one side of which measures 20 cm and one diagonal 24 cm.
Answer: 384 \(cm^2\)

Question. The difference between two parallel sides of a trapezium is 4 cm. The perpendicular distance between them is 19 cm. If the area of the trapezium is 475 \(cm^2\), find the lengths of the parallel sides.
Answer: 27 cm, 23 cm

Question. Find the length of a rope by which a cow must be tethered in order that it may be able to graze an area of 9856 sq. metres.
Answer: 56 m

Question. The area of a circular field is 13.86 hectares. Find the cost of fencing it at the rate of Rs. 4.40 per metre.
Answer: 5808

Question. The diameter of the driving wheel of a bus is 140 cm. How many revolutions per minute must the wheel make in order to keep a speed of 66 kmph?
Answer: 250

Question. A wheel makes 1000 revolutions in covering a distance of 88 km. Find the radius of the wheel.
Answer: 14 m

Question. The inner circumference of a circular race trak, 14 m wide, is 440 m. Find the radius of the outer circle.
Answer: 84 m

Question. A sector of 120º, cut out from a circle, has an area of \(9 \frac{3}{7}\) sq. cm. Find the radius of the cirlce.
Answer: 3 cm

Question. Find the ratio of the areas of the incircle and circumcircle of a square.
Answer: \(1 : 2\)

Question. Find the volume and surface area of a cuboid 16 m long, 14 m broad and 7 m high.
Answer: 868 \(m^2\)

Question. Find the length of the longest pole that can be placed in a room 12 m long, 8 m broad and 9 m high.
Answer: 17 m

Question. The volume of a wall, 5 times as high as it is borad and 8 times as long as it is high, is 12.8 cu. metres. Find the breadth of the wall.
Answer: 40 cm

Question. Find the number of bricks, each measuring 24 cm × 12 cm × 8 cm, required to construct a wall 24 m long, 8 m high and 60 cm thick, if 10% of the wall is filled with mortar ?
Answer: 45000

Question. Water flows into a tank 200 m × 150 m through a rectangular pipe 1.5 m × 1.25 m @ 20 kmph. In what time (in minutes) will the water rise by 2 metres?
Answer: 96 min.

Question. The dimensions of an open box are 50 cm, 40 cm and 23 cm. Its thickness is 3 cm. If 1 cubic cm of metal used in the box weighs 0.5 gms, find the weight of the box.
Answer: 8.04 kg.

Question. The diagonal of a cube is \(6\sqrt{3}\) cm. Find its volume and surface area.
Answer: 216 \(cm^3\), 216 \(cm^2\)

Question. The surface area of a cube is 1734 sq. cm. Find its volume.
Answer: 4913 \(cm^3\)

Question. A rectangular block 6 cm by 12 cm by 15 cm is cut up into an exact number of eqaul cubes. Find the least possible number of cubes.
Answer: 40

Question. A cube of edge 15 cm is immersed completely in a rectangular vessel containing water. If the dimensions of the base of vessel are 20 cm × 15 cm, find the rise in water level.
Answer: 11.25 cm

Question. Three solid cubes of sides 1 cm, 6 cm and 8 cm are melted to form anew cube. Find the surface area of the cube so formed.
Answer: 486 \(cm^2\)

Question. If each edge of a cube is increased by 50%, find the percentage increase in its surface area.
Answer: 125%

Question. Two cubes have their volumes in the ratio \(1 : 27\). Find the ratio of their surface areas.
Answer: \(1 : 9\)

Question. Find the volume, curved surface area and the total surface area of a cylinder with diameter of base 7 cm and height 40 cm.
Answer: 1540 \(cm^3\), 880 \(cm^2\), 957 \(cm^2\)

Question. If the capacity of a cylindrical tank is 1848 \(m^3\) and the diameter of its base is 14 m, then find the depth of the tank.
Answer: 12 m

Question. 2.2 cubic dm of lead is to be drawn into a cylindrical wire 0.50 cm in diameter. Find the length of the wire in metres.
Answer: 112 m

Question. How many iron rods, each of length 7 m and diameter 2 cm can be made out of 0.88 cubic metre of iron?
Answer: 400

Question. The radii of two cylinders are in the ratio \(3 : 5\) and their heights are in the ratio of \(2 : 3\). Find the ratio of their curved surface areas.
Answer: \(2 : 5\)

Question. If 1 cubic cm of cast iron weighs 21 gms, then find the weight of a cast iron pipe of length 1 metre with a bore of 3 cm and in which thickness of the metal is 1 cm.
Answer: 26.4 kg

Question. Find the slant height, volume, curved surface area and the whole surface area of a cone of radius 21 cm and height 28 cm.
Answer: 12936 \(cm^3\), 2310 \(cm^2\), 3696 \(cm^2\)

Question. Find the length of canvas 1.25 m wide required to build a conical tent of base radius 7 metres and height 24 metres.
Answer: 440 m

Question. The heights of two right circular cones are in the ratio \(1 : 2\) and the permieters of their bases are in the ratio \(3 : 4\). Find the ratio of their volumes.
Answer: \(9 : 32\)

Question. The radii of the bases of a cylinder and a cone are in the ratio of \(3 : 4\) and their heights are in the ratio of \(2 : 3\). Find the ratio of their volumes.
Answer: \(9 : 8\)

Question. A conical vessel, whose internal radius is 12 cm and height 50 cm, is full of liquid. The contents are emptied into a cylindrical vessel with internal radius 10 cm. Find the height to which the liquid rises in the cylindrical vessel.
Answer: 24 cm

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