(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

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 m^{2} - 12 mn + 4^{2}

= (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

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 |

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