# Free Mensuration 01 Practice Test - 8th Grade

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).

A.

20 tiles

B.

25 tiles

C.

35 tiles

D.

50 tiles

#### SOLUTION

Solution : B

Number of tiles required
= area of the floorarea of one tile
= (30×50)(10×6)
= 25 tiles

A rectangular playground is 60 m long and breadth of the field is 25 m, its area is 150 m2.

A.

True

B.

False

#### SOLUTION

Solution : B

Area of the rectangular playground = length × breadth

= 60 × 25 = 1500 m2.

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)?

A.

36 m2

B.

72 m2

C.

96 m2

D.

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 rectangle

4a = 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

The perimeter of above shown figure is 9.5 cm. State whether the given answer is true or false.

A.

True

B.

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.

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).

A.

100

B.

200

C.

250

D.

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

___ cm is the height of a cylinder whose radius is 14 cm and the total surface area is 2640 sq.cm

#### 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 h

2640 = 2 x 227 x (14)2 + 2 x 227 x(14) h .

Hence, h = 16 cm.

The formula for finding the total surface area of a cuboid is __________.

A.

2×(lb×bh×hl)

B.

2×(lb+bh+hl)

C.

2h×(l+b)

D.

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).

The area of four walls of a cube whose one edge is 2.5 m is 25 m2.

A.

True

B.

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

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.

A.

280 cm2

B.

284 cm2

C.

286 cm2

D.

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 cube

Let 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.

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.

A.

40 m

B.

50 m

C.

60 m

D.

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