6TH GRADE MATH PRACTICE QUIZ

(1)  Fill in the boxes.

(2)  A car travels 432 km on 48 liters of petrol. How far would it travel on 20 liters of petrol?

(3)  An electric pole, 24 meters high casts a shadow of 20 meters. Find the height of a tree. If it casts a shadow of 15 meters under similar conditions

(4)  A train 315 m long is running at 54 km/h.How much time will it take to cross a pole?

(5)  In an examination John secured 372 marks. If she secured 62% marks, find the maximum marks.

(6)  Factorize  9 m² + 4² -12 mn

(7)  Length of a rectangle is 8m less than twice its width. If the perimeter of the rectangle is 56m, find the length and width

(8)  The length of the sides of a right triangle are 6 cm and 8 cm. What is the length of its hypotenuse?

(9)  A rectangular lawn of length 40 m and width 25 m is to be surrounded externally by a path which is 2m wide. Find the area of the path.

(10)  Capacity of a tank is 60 m³. If the length and width of the tank are 5 m and 4 m respectively, find its depth.

6th grade worksheet - Solution

Question 1 :

Fill in the boxes.

Solution :

Let the two unknowns be "a" and "b"

90/165  =  -6/a

Since it is equivalent fraction, 

90(a)  =  -6(165)

In order to find the value of "a", we have to divide by 90 on both sides.

90a/90  =  -6(165)/90

a  =  -11

Like wise,

90/165  =  b/-55

Since it is equivalent fraction, 

90 (-55)  =  b (165)

By dividing 165 on both sides, we get

90(-55)/165  =  165b/165

b  =  -30

So, the answer is -11 & -30.

Question 2 :

A car travels 432 km on 48 liters of petrol. How far would it travel on 20 liters of petrol?

Solution :

Since the petrol consumption is getting decreased, number of km they traveled also will also get decrease.

Hence this come under direct variation.

So,

432 (20)  =  x (48)

By dividing 48 on both sides, we get

432(20) / 48  =  48x / 48

x  =  180 km

So, the answer is 180 km.

Question 3 :

An electric pole, 24 meters high casts a shadow of 20 meters. Find the height of a tree. If it casts a shadow of 15 meters under similar conditions

Solution :

Let x be the required length of pole

24/x  =  20/15

Multiply by x on both sides, we get

(24/x) x  =  4x/3

24  =  4x/3

Multiply by 3 on both sides,

24(3)  =  4x

Divide by 4 on both sides

24(3)/4  =  x

 6(3)  =  x 

x  =  18 m

Question 4 :

A train 315 m long is running at 54 km/h.How much time will it take to cross a pole?

Solution :

Given length of train = 315 m

That is distance travelled by the train to completely cross the pole = 315 m

Speed of train = 54 km/hr

= 54 x (5/18) = 15 m/sec

We know that, time taken = distance / speed

= 315/15

= 21 seconds

Thus the train takes 21 seconds to cross the pole.

Question 5 :

In an examination John secured 372 marks. If she secured 62% marks, find the maximum marks.

Solution :

Marks secured by John  =  372

Let the total marks be x. 

 62% of x   =  372 

(62/100) x   =  372

0.62 x  =  372

Dividing 0.62 on both sides, we get

0.62x / 0.62  =  372 / 0.62

x  =  600

Question 6 :

Factorize  9 m² + 4² -12 mn

Solution :

  =  9 m²  - 12 mn + 4²

  =  (3 m)²  - 2(3m)(2)  + 2²

The above line exactly matches with the algebraic identity a² - 2ab + b²

a² - 2ab + b²  =  (a - b)²

  =  (3m - 2)²

Question 7 :

Length of a rectangle is 8m less than twice its width. If the perimeter of the rectangle is 56m, find the length and width

Solution :

Let x be the width of the rectangle.

length  =  2x - 8

Perimeter of the rectangle  =  56 m

2(l + w)  =  56

2(2x - 8 + x)  =  56

2 (3x  - 8)  =  56

Divide by 2 on both sides, we get

3x - 8  =  56/2

3x - 8  =  28

Add 8 on both sides

3x  =  36

Divide by 3 on both sides

x  =  12 and  2x - 8  ==>  2(12) - 8  ==>  16 cm

So, the width is 12 cm and length is 16 cm.

Question 8 :

The length of the sides of a right triangle are 6 cm and 8 cm. What is the length of its hypotenuse?

Solution :

(hypotenuse)²  =  Sum of squares of other two sides

(hypotenuse)²  =  6² + 8²

  =  36  + 64

  =  100

Hypotenuse  =  √100  =  10 cm.

Question 9 :

A rectangular lawn of length 40 m and width 25 m is to be surrounded externally by a path which is 2m wide. Find the area of the path.

Solution :

Since the path surrounded externally, the length and width of rectangular portion including the path will be 4m more than the lawn.

length of path  = 40 + 2 + 2  =  44 m

width of path  =  25 + 2 + 2  =  29 m

Area of path  =  44(29)  -  40(25)

  =  1276  -  1000

  =  276m²

Question 10 :

Capacity of a tank is 60 m³. If the length and width of the tank are 5 m and 4 m respectively, find its depth.

Solution :

From the above information, we come to know that the tank is in the form of cuboid.

capacity of tank  =  60 m³

length x width x breadth  =  60

5 x 4 x depth  =  60

depth  =  60/20

depth  =  3 m

So, the answer is 3 m. 6th grade worksheet  6th grade worksheet

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