An aluminium sphere of $20 \; cm$ diameter is heated from $0^{\circ} C$ to $100^{\circ} C$. Its volume changes by (given that coefficient of linear expansion for aluminium $\alpha_{Al} = 23 \times 10^{-6} \; /^{\circ} C$): (in $; cm^3$)

Two rods $A$ and $B$ of identical dimensions are at temperature $30\,^{\circ}C$. If $A$ is heated up to $180\,^{\circ}C$ and $B$ up to $T\,^{\circ}C$,then the new lengths are the same. If the ratio of the coefficients of linear expansion of $A$ and $B$ is $4:3$,then the value of $T$ is........$^{\circ}C$.

$A$ thin rod having length $L_0$ at $0\,^{\circ}C$ and coefficient of linear expansion $\alpha$ has its two ends maintained at temperatures $\theta_1$ and $\theta_2$,respectively. Find its new length.

$A$ $1$ litre glass flask contains some mercury. It is found that at different temperatures,the volume of air inside the flask remains the same. What is the volume of mercury in this flask in $cc$ if the coefficient of linear expansion of glass is $9 \times 10^{-6} /^{\circ}C$ and the coefficient of volume expansion of mercury is $1.8 \times 10^{-4} /^{\circ}C$?

$A$ thin copper wire of length $l$ meters is heated by $10^{\circ}C$,resulting in a $2\%$ increase in its length. If a square copper sheet of side $l$ meters is heated by the same $10^{\circ}C$,what is the percentage change in its area?

$A$ solid ball of metal has a concentric spherical cavity within it. If the ball is heated,the volume of the cavity will