Cone, a hemisphere and a cylinder stand o… | Answer

Subject

Quantitative Aptitude

Topic

Mensuration

Cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes are:
Reading

ক)

1:2:2

খ)

1:2:3

গ)

1:2:4

ঘ)

2:3:4

ঙ)

3:2:4

Explanation

Since the Cone, hemisphere and cylinder have same radius and same height Volume of the cone is given by

= {\rm{\;}}\frac{1}{3}{\rm{\pi }}{{\rm{r}}^2}{\rm{h}}

Volume of the hemisphere is given by

= \frac{2}{3}{\rm{\pi }}{{\rm{r}}^3}

Volume of the cylinder is given by = πr 2 h ∴ Ratio of their volumes = Volume of the cone: Volume of the hemisphere: Volume of the cylinder ∴ Ratio of their volumes

= {\rm{\;}}\frac{1}{3}{\rm{\pi }}{{\rm{r}}^2}{\rm{h\;}}:{\rm{\;}}\frac{2}{3}{\rm{\pi }}{{\rm{r}}^3}:{\rm{\pi }}{{\rm{r}}^2}{\rm{h\;}}

[∵ r = h] ⟹ Ratio of their volumes

= {\rm{\;}}\frac{1}{3}{\rm{\;}}:{\rm{\;}}\frac{2}{3}:1 = 1:2:3

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Cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes are:Reading

Cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes are:

Explanation

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Cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes are:
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