Free Mensuration 01 Practice Test - 8th Grade
Question 1
A flooring tile has the shape of a rectangle whose dimensions are 10cm × 6cm. How many such tiles are required to cover a floor of area 30 × 50 cm2? (If required you can split the tiles in whatever way you want to fill up the corners).
20 tiles
25 tiles
35 tiles
50 tiles
SOLUTION
Solution : B
Number of tiles required
= area of the floorarea of one tile
= (30×50)(10×6)
= 25 tiles
Question 2
A rectangular playground is 60 m long and breadth of the field is 25 m, its area is 150 m2.
True
False
SOLUTION
Solution : B
Area of the rectangular playground = length × breadth
= 60 × 25 = 1500 m2.
Question 3
If a square of side 8m and a rectangle of length 12m have the same perimeter, then find the area of the rectangle(in m2)?
36 m2
72 m2
96 m2
48 m2
SOLUTION
Solution : D
Let the side of a square be 'a' and length and breadth of a rectangle be 'l' and 'b' respectively.
Given,
Perimeter of square = Perimeter of rectangle4a = 2(l +b)
4 × 8 = 2(12 + b)
32 = 24 + 2b
8 = 2b
Hence b = 4 m
Area of rectangle = l × b = 12 × 4 = 48 m2
Question 4
The perimeter of above shown figure is 9.5 cm. State whether the given answer is true or false.
True
False
SOLUTION
Solution : A
The perimeter of the figure given above is the sum of arc length BC + length AB + length AC.
Perimeter of the given shape = πr + 2 + 2 = [227 × 3.52 ] + 4= 5.5 + 4 = 9.5 cm
Hence, it is true.
Question 5
The diagonal of a trapezium shaped field is 25m and the perpendiculars dropped on it from the remaining opposite vertices are 8m and 12m. Find the area of the field(in m2).
100
200
250
300
SOLUTION
Solution : C
We can calculate the area of this quadrilateral as the sum of the areas of two triangles taking diagonal length 25m as the base for both triangles and perpendicular length 8m as the height of one triangle and the perpendicular length 12m as the height of another triangle.
Area of triangle = 12×base×height
Area of the first triangle = 12×25×8
Area of the second triangle = 12×25×12
Area of quadrilateral = Area of the first triangle + Area of the second triangle
Area of quadrilateral = 12(25)(8+12)=250m2
Question 6
SOLUTION
Solution :Given, the radius (r) is 14cm.
Let h be the height of the cylinder.
Total surface area of cylinder = 2 π r2 + 2 π r h2640 = 2 x 227 x (14)2 + 2 x 227 x(14) h .
Hence, h = 16 cm.
Question 7
The formula for finding the total surface area of a cuboid is __________.
2×(lb×bh×hl)
2×(lb+bh+hl)
2h×(l+b)
2×lb×(bh+hl)
SOLUTION
Solution : B
Let l be the length, b be the breadth and h be the height of a cuboid.
The formula for finding the total surface area of the cuboid is 2×(lb+bh+hl).
Question 8
The area of four walls of a cube whose one edge is 2.5 m is 25 m2.
True
False
SOLUTION
Solution : A
Edge of the cube (a) = 2.5 m
Area of four walls = 4a2
= 4 x 2.5 x 2.5 m2 = 25 m2
Question 9
A metal sheet 27 cm long, 8 cm broad and 1 cm thick is melted into a cube. The difference between total surface area of the two solids is ______ cm2.
280 cm2
284 cm2
286 cm2
296 cm2
SOLUTION
Solution : C
The metal sheet is in the shape of a cuboid.
Total surface area of the cuboid is given by 2 (lb + bh + hl) = 2[(27 ×8) + (8 ×1) + (1 ×27)] = 502 cm2.When the metal sheet is melted into a cube, then the volume of the metal sheet will be equal to the volume of the cube.
Hence, Volume of the cuboid = Volume of the cubeLet each side of the cube be a
Hence, 27 × 8 × 1 = a3
⇒a = 6 cm
Total Surface area of the cube is given by 6a2 = 6 × (6)2 = 216 cm2.
Hence, the difference between surface areas of two solids = (502 -216) cm2 = 286 cm2.
Question 10
The area of a trapezium shaped field is 600 m2, the distance between two parallel sides is 15 m and one of the parallel side is 20 m. Find the length of the other parallel side.
40 m
50 m
60 m
70 m
SOLUTION
Solution : C
Let the length of the other parallel side be a.
Given, one of the sides is 20 m and the distance between two parallel sides is 15 m.
The area of trapezium is given by
=12× Sum of the length of the two parallel sides × Distance between the two parallel sides.
Hence,600 = 12 (a + 20) × 15
a + 20 = 80
a = 80 – 20 = 60
Hence, the length of the other parallel side = 60 m