Two cubes each of volume 27 cm³ are joined end to end to form a solid . Find the surface area of the resulting cuboid

OR

A cone of height 20cm and radius of base 5cm is made up of modelling clay. A child reshapes it in form of a sphere. Find the diameter of the sphere

We know,

Volume of cube = L³

Where L is the length of the side of the cube.

Given, Volume of one cube = 27 cm³

⇒ L³ = 27cm³

⇒ L = 3 cm

So, when two cubes are joined together, resulting side of the cuboid is

Length, L = 3 + 3 = 6 cm

Breadth, B = 3 cm

Height, H = 3 cm

Total Surface area of a cuboid = 2(LB + BH + HL)

= (2 × 6 × 3) + (2 × 3 × 3) + (2 × 3 × 3)

= 36 + 18 + 18

= 36 + 36

= 72cm²

Surface area of resulting cuboid is 72 cm²

OR

Volume will be same for both cone and sphere

V₁ is volume of the cone

V₂ is the volume of the sphere

R₁ is the radius of the cone = 5cm

R₂ is the volume of the sphere

H is the height of the cone = 20cm

We know,

Volume of cone , where r and h are base radius and height respectively.

Volume of Sphere, where r is the radius of sphere.

Volume will remain same so,

⇒ V₁ = V₂

⇒

⇒ π(R₁)²H = 4π(R₂)³

⇒ (R₁)²H = 4(R₂)³

Now substituting the values, we get

⇒ 5² × 20 = 4(R₂)³

⇒ 5 × 5 × 5 × 4 = 4(R₂)³

⇒ R₂ = 5cm

⇒ Diameter = 2 × Radius = 10 cm

Hence diameter of the sphere is 10 cm.