Question

LONG TYPE QUESTIONS

Q1. If each edge of a cube is doubled,

i) How many times will its surface area increase?

ii) How many times will its volume increase?​

Answer 1

Given:-

• If each edge of a cube is Doubled

To Find:-

• How many times will its surface area increases.

• How many times will it's Volume increase.

Formulae used:-

• Surface area of Cube = 6a²

• Volume of cube = (side)³

Now,

If the edge of cube is doubled then the each edge becomes 2a.

Now,

→ Surface area of cube (s¹) = 6a²

After doubling the edge of a each cube.

→ New surface area of cube = 6(2a)²

→ New surface area of cube(S²) = 6 × 4a² = 24a².

→ Increase in surface area = S² - S¹/S¹

→ $\rm{\dfrac{ 24a^2 - 6a^2}{6a^2}\times{100}}$

→ $\rm{\dfrac{\cancel{18a^2}}{\cancel{6a^2}}\times{100}}$

→ $\rm{3\times{100}}$

→ $\rm{300}$

Hence, Increase in Surface area will be 300%.

Therefore,

→ Volume of cube ( v¹) = (a)³

After Doubling the edges of cube

→ Volume of cube= (2a)³

→ Volume of cube (V²)= 8a³

→ Increase in Volume = V² - V¹/ V¹ × 100

→ $\rm{\dfrac{8a^3 - a^3}{a^3}}$

→ $\rm{\dfrac{ 7\cancel{a^3}}{\cancel{a^3}}\times{100}}$

→ $\rm{ 7\times{100}}$.

→ $\rm{ 700}$.

Thus, Increase in Volume of cube is 700%