**6th grade worksheet :**

Here you can find 10 problems on math which are in the level of 6 th grade

(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.

**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

Hence 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

Hence 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

Hence 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

Hence the answer is 3 m. 6th grade worksheet 6th grade worksheet

These are the question in the topic 6th grade worksheet.

Answers

1. -11 & -30

2. 180 km

3. 18 m

4. 21 seconds

5. 600

6. (3m-2n) (3m-2n)

7. 16 m & 12 m

8. 10 cm

9. 276 m²

10. 3 m

After having gone through the stuff given above, we hope that the students would have understood "6th grade worksheet"

Apart from the stuff given above, if you want to know more about "6th grade worksheet, please click here.

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

You can also visit our following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**