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Mensuration — MATHS STD 8 — Question

Gujarat BoardEnglish MediumSTD 8MATHSMensuration1 Mark
MCQ
Ramesh has three containers.
$a.$ Cylindrical container $A$ having radius $r$ and height $h,$
$b.$ Cylindrical container $B$ having radius $2r$ and height $\frac{1}{2} h.$
$c.$ Cuboidal container $C$ having dimensions $r \times r \times h.$
The arrangement of the containers in the increasing order of their volumes is:
  • A
    $A, B, C$.
  • B
    $B, C, A.$
  • ✓
    $C, A, B.$
  • D
    cannot be arranged.
✓

Answer

Correct option: C.
$C, A, B.$
$i.$ The volume of the cylindrical container having radius $r$ and height $h =\pi\text{r}^2\text{h}$
$ii.$ The volume of the cylindrical container with radius $2r$ and height $\frac{1}{2}=\pi(2\text{r})^2\times\frac{1}{2}\text{h}$
$=\pi\times4\text{r}^2\times\frac{1}{2}\text{h}$

$=2\pi\text{r}^2\text{h}$
$iii.$ The volume of the cuboidal container having dimensions $r \times r \times h = r^2h$
$iv.$ From parts $(i), (ii)$ and $(iii),$ we have the following order $C, A, B.$

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