# SOLVING MENSURATION WORD PROBLEMS WITH THE SHAPE CUBE

## About "Solving Mensuration Word Problems with the Shape Cube"

Solving Mensuration Word Problems with the Shape Cube :

Here we are going to see some practice questions on solving mensuration word problems with the shape cube.

If the side of a cube is a units, then,

Then

(i) The Total Surface Area = 6a2 sq.units

(ii) The Lateral Surface Area = 4a2 sq.units

(iii)  Volume  =  a3

## Solving Mensuration Word Problems with the Shape Cube - Practice questions

Question 1 :

Find the TSA and LSA of the cube whose side is

(i) 8 m (ii) 21 cm (iii) 7.5 cm

Solution :

Total surface area  =  6a2

Side length (a)  =  8 m

=  6(8)2

=  6(64)

=  384 m2

Lateral surface area  =  4a2

Side length (a)  =  8 m

=  4(8)2

=  4(64)

=  256 m2

(ii) 21 cm

Total surface area  =  6a2

Side length (a)  =  21 cm

=  6(21)2

=  6(441)

=  2646 cm2

Lateral surface area  =  4a2

Side length (a)  =  21 cm

=  4(21)2

=  4(441)

=  1764cm2

(iii)  7.5 cm

Total surface area  =  6a2

Side length (a)  =  7.5 cm

=  6(7.5)2

=  6(56.25)

=  337.5 cm2

Lateral surface area  =  4a2

Side length (a)  =  7.5 cm

=  4(7.5)2

=  4(56.25)

=  225 cm2

Question 2 :

If the total surface area of a cube is 2400 cm2 then, find its lateral surface area.

Solution :

Total surface area  =  2400

6a2  =  2400

a2  =  2400/6

a2  =  400

a  =  20 cm

Lateral surface area  =  4a2

=  4(20)2

=  4(400)

=  1600 cm2

Question 3 :

A cubical container of side 6.5 m is to be painted on the entire outer surface. Find the area to be painted and the total cost of painting it at the rate of ₹24 per m2.

Solution :

Side length of cubical container  =  6.5 m

Curved surface area of container  =  6a2

=  6(6.5)2

=  6(42.25)

=  253.5 m2

Cost of painting   =  ₹24 per m2

Required cost  =  253.5 (24)

=  ₹ 6084

Question 4 :

Three identical cubes of side 4 cm are joined end to end. Find the total surface area and lateral surface area of the new resulting cuboid.

Solution :

Curved surface area of resulting cuboid  =  2h(l + b)

length of resulting cuboid  =  4 + 4 + 4  =  12 cm

breadth of cuboid  =  4 cm and height of cuboid  =  4 cm

=  2 (4) (12 + 4)

=  8(16)

=  128 cm2

Total surface area   2 (lb + bh + hl)

=  2[12(4) + 4(4) + 4(12)]

=  2 [ 48 + 16 + 48 ]

=  2(112)

=  224 cm2 After having gone through the stuff given above, we hope that the students would have understood, "Solving Mensuration Word Problems with the Shape Cube"

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