Question

The radii of two solid iron spheres are $1cm$ and $6cm$ respectively. A hollow sphere is made by melting the two spheres. If the external radius of the hollow sphere is $9cm$, then its thickness (in cm) is

• A. $2$
• B. $0.5$
• C. $1$
• D. $1.5$
• E. $Noneofthese$

Answer 1

The correct option is C $1$

Volume of a sphere$=\frac{4}{3}\pi r^3$

Total volume of two spheres$=\frac{4}{3}\pi (1^3+6^3)$

Let internal radius of hollow sphere$=rcm$ then

Volume of the iron of this sphere$=\frac{4}{3}\pi (9^3-r^3)cu.cm$

According to the question,

$\frac{4}{3}\pi (1^3+6^3)=\frac{4}{3}\pi (9^3-r^3)$

$1+6^3=9^3-r^3$

$r^3=9^3-6^3-1=729-216-1=512$

$\Rightarrow r=\sqrt[3]{3512}=8cm$

$\therefore Thickness=Externalradius-internalradius=9-8=1cm$