Question

A solid metal sphere of volume 1280cm3 is melted down and recast into 20 equal solid cubes find the length of each side

Answer 1

Answer:

Given –

• Volume of the metal sphere = 1280 cm³.
• It has been melted and recast into 20 cubes.
• The sides of the cubes are equal.

To prove –

• Length of each side.

Solution –

Here, we can say that volume of the sphere equals volume of 20 cubes.

➸ Volume of sphere = 20 * Volume of one cube

➸ 1280 cm³ = 20 * a³

➸ a³ = 1280/20

➸ a³ = 128/2

➸ a³ = 64

➸ a = cube root of 64

➸ a = 4

Hence, side length of one cube is 4 cm.

FORMULAS :–

• Volume of cube = a³.
• Volume of cuboid = lbh.
• Volume of sphere = 4/3 πr³.
• Volume of hemisphere = 2/3 πr³.
• Volume of cone = ⅓πr²h.
• Volume of cylinder = πr²h.

Answer 2

$\huge\sf\red{Answer:}$

☆ Given:

⇒ A solid metal sphere of volume 1280 cm³ is melted down and recast into 20 equal solid cubes.

☆ Find:

⇒ Find the length of each side.

Using formula:

⇒ $\sf Volume \: of \: cube = a^3$

⇒ $\sf Volume \: of \: sphere = 20 \times a^3$

☆ Calculations:

⇒ $\sf 1280 cm^3 = 20 \times a^3$

⇒ $\sf a^3 = \cancel{\dfrac{1280}{20}}$

⇒ $\sf a^3 = \cancel{ \dfrac{128}{2}}$

⇒ $\sf a^3 = 64$

⇒ $\sf a = \sqrt[]{64}$

⇒ ${\sf{\underline{\boxed{\green{\sf{ a = 4}}}}}}$

Therefore, 4 is the length of each side.