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Surface Areas and Volumes — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsSurface Areas and Volumes1 Mark
MCQ
A solid consists of a circular cylinder with an exact fitting right circular cone placed at the top. The height of the cone is h. If the total volume of the solid is 3 times the volume of the cone, then the height of the circular is:
  • A
    $2\text{h}$
  • ✓
    $\frac{2\text{h}}{3}$
  • C
    $\frac{3\text{h}}{2}$
  • D
    $4\text{h}$
✓

Answer

Correct option: B.
$\frac{2\text{h}}{3}$

Let r be the radius of the base of solid.
Clearly,
The volume of solid = 3 × volume of cone
Vol. of cone + Vol. of cylinder = 3 Volume of cone
Vol. of cylinder = 2 Vol. of cone
$\pi\text{r}^2\text{x}=2\times\frac{1}{3}\pi\text{r}^2\text{h}$
$\text{x}=\frac{2}{3}\text{h}$
Thus,
The height of cylinder $=\frac{2}{3}\text{h}$

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