Volume and Surface Area of Cube and Cuboid

Here we will learn how to solve the problems on Volume and Surface Area of Cube and Cuboid:

1. Two cubes of edge 14 cm each are joined end to end to form a cuboid. Find the volume and the total surface area of the cuboid.

Solution:

The volume of the cuboid = 2 × volume of one cube

= 2 × 14$$^{3}$$ cm$$^{3}$$

= 5488 cm$$^{3}$$

The total surface area of the cuboid = 2(28 × 14 + 14 × 14 + 14 × 28) cm$$^{2}$$

= 2(28 + 14 + 28) × 14 cm$$^{2}$$

= 2(2 × 14 + 1 × 14 + 2 × 14) × 14 cm$$^{2}$$

= 2(2 + 1 + 2) × 14 × 14 cm$$^{2}$$

= 2(5) × 14 × 14 cm$$^{2}$$

= 10× 14 × 14 cm$$^{2}$$

= 1960 cm$$^{2}$$

2. The dimensions of the base of a rectangular vessel are 60 cm × 45 cm. Its height is 20 cm. The vessel is half-filled with water. What should be the size of a solid iron cube which when dropped into the vessel will raise the water level up to the brim?

Solution:

The volume of the vessel = 60 × 45 × 20 cm$$^{3}$$

= 54000 cm(^{3}\)

It is half-filled with water

So, the volume of the empty portion of the vessel = $$\frac{1}{2}$$ × 54000 cm$$^{3}$$

= 27000 cm$$^{3}$$

The volume of the iron cube should be 27000 cm$$^{3}$$ so that it displaces this amount of water and the water level comes up to the brim.

If the edge of the cube is x then,

x$$^{3}$$ = 27000 cm$$^{3}$$

⟹ x$$^{3}$$ = (30)$$^{3}$$ cm$$^{3}$$

⟹ x = 30 cm

Therefore, the edge of the iron cube = 30 cm

The size of the cube should be 30 cm × 30 cm × 30 cm.

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