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.

9th Grade Math

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