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If n coins each of diameter 1.5 cm and thickness 0.2 cm are melted and a right circular cylinder of height 10 cm and diameter is 4.5 cm is made then n =
(A) 336
(B) 450
(C) 512
(D) 545.

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Last updated date: 20th Jun 2024
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Answer
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Hint: Here, we know that
the volume of right circular cylinder = n × volume of 1.5 cm diameter coin.
Where, volume of right circular cylinder = $\text{ }\!\!\pi\!\!\text{ }{{\text{r}}^{2}}\text{h}$
Where r = radius and h = height

Complete step by step solution: Given that,
⇒ diameter of coin = 1.5 cm.
⇒ height of cylinder = 10 cm.
⇒ diameter of cylinder = 4.5 cm.
Now,
Let n be the number of 1.5 cm diameter coins required to form a right circular cylinder of height 10 cm and diameter 4.5 cm.
Now,
According to the question,
⇒ The volume of right circular cylinder = n × volume of 1.5 cm diameter coin
⇒ We know that,
Volume of cylinder = $\text{ }\!\!\pi\!\!\text{ }{{\text{r}}^{2}}\text{h}$.
Where r = radius
h = height of cylinder.
Now,
$\Rightarrow \text{ }\!\!\pi\!\!\text{ }{{\text{r}}^{2}}\text{h}\,\text{=}\,\text{n}\times \text{ }\!\!\pi\!\!\text{ }\,{{\left( \dfrac{1.5}{2} \right)}^{2}}\times 0.2$
⇒ After dividing, we get,
⇒ $\text{n}=\dfrac{\text{ }\!\!\pi\!\!\text{ }{{\left( \dfrac{4.5}{2} \right)}^{2}}\times 10}{\text{ }\!\!\pi\!\!\text{ }{{\left( \dfrac{1.5}{2} \right)}^{2}}\times \dfrac{2}{10}}$
After dividing, we get
⇒ n = 9 × 10 × 5

⇒ n = 450

Note: in this type of question we know about the right circula cylinder that is a cylinder with the bases circular and with the axis joining the two centers of the bases perpendicular to the planes of the two bases. Here, we know that volume of right circular cylinder = $\pi\text{r}^{2}\text{h}$ and then take volume of right circular cylinder = n × volume of 1.5 cm diameter coin
⇒ $\text{ }\!\!\pi\!\!\text{ }{{\text{r}}^{2}}\text{h}=\text{n}\times \text{ }\!\!\pi\!\!\text{ }{{\left( \dfrac{1.5}{2} \right)}^{2}}\times 0.2$