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Surface Areas and Volumes — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsSurface Areas and Volumes1 Mark
Question
Write ‘True’ or ‘False’ and justify your answer in the following:
A solid ball is exactly fitted inside the cubical box of side a. The volume of the ball is $\frac{4}{3}\pi\text{a}^3.$
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Answer

False: Clearly from figure when ball (spherical) is exatly fitted inside the cubical box then diameter of the ball becomes equal to side of cube so
Diameter = d = a $\Rightarrow\ \ \text{Radius}=\text{r}=\frac{\text{a}}{2}$ $\therefore$ Volume of spherical ball $=\frac{4}{3}\pi\text{r}^3$ $=\frac{4}{3}\pi\Big(\frac{\text{a}}{2}\Big)=\frac{4}{3}\pi\frac{\text{a}^3}{8}=\frac{1}{6}\pi\text{a}^3\neq\frac{4}{3}\pi\text{a}^3$ Hence, the given statement is false.

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