A single solid sphere is melted into thre… | Answer

Subject

Quantitative Aptitude

Topic

Mensuration

ক)

9 cm

খ)

7.5 cm

গ)

5 cm

ঘ)

6 cm

ঙ)

None of these

Let the radius of the original sphere be r ∴ Volume of the solid sphere is given by

= \frac{4}{3}\pi {r^3}

∴ Volume of the first solid sphere

= \frac{4}{3}\pi {\left( 1 \right)^3}

∴ Volume of the second solid sphere

= \frac{4}{3}\pi {\left( 6 \right)^3}

∴ Volume of the third solid sphere

= \frac{4}{3}\pi {\left( 8 \right)^3}

Since a single sphere is melted into three solid sphere ∴ Volume of the original solid sphere = Volume of the three smaller solid spheres

\therefore {\rm{\;}}\frac{4}{3}\pi {r^3} = {\rm{\;}}\frac{4}{3}\pi {\left( 1 \right)^3} + {\rm{\;}}\frac{4}{3}\pi {\left( 6 \right)^3} + {\rm{\;}}\frac{4}{3}\pi {\left( 8 \right)^3}

⟹ r 3 = 1 3 + 6 3 + 8 3 ⟹ r 3 = 729 ⟹ r = 9 cm ∴ Radius of the original sphere (r) = 9 cm

A single solid sphere is melted into three solid spheres of lead whose radii are 1 cm, 6 cm, 8 cm respectively. Find the radius of the original sphere