Question

Two cylinderical cams have same bases of diameter 21 cm.If one of them is 12 cm high and the other is 18 cm then find the ratio of their volumes​

Answer 1

$\red{\Large\underline{\underline\mathtt{Question:}}}$

Two cylinderical cans have same bases of diameter 21 cm. If one of them is 12 cm high and the other is 18 cm then, find the ratio of their volumes.

$\blue{\Large\underline{\underline\mathtt{To\:Find:}}}$

～> Ratio of the volumes of the two cylinder.

$\green{\Large\underline{\underline\mathtt{Given:}}}$

• Diameter of the two cylinders = 21 cm
• Height $\rightarrow h_{1} = 12 cm$
• Height $\rightarrow h_{2} = 18 cm$

$\red{\Large\underline{\underline\mathtt{We\:know:}}}$

☞✧Volume of the Cylinder ✧

$\purple{\sf{\underline{\boxed{V_{c} = \pi\:r^{2}h}}}}$

$\blue{\Large\underline{\underline\mathtt{Concept:}}}$

In this case , by comparing the two volumes of the given cylinder we can find the ratio of there volumes......

$\green{\Large\underline{\underline\mathtt{Solution:}}}$

By comparing the two volumes, we get

$\purple{\sf{V_{1} : V_{2}}}$

$\purple{\sf{\pi\:r^{2}h_{1} : \pi\:r^{2}h_{2}}}$

$\purple{\sf{\cancel{\pi}\:\cancel{r^{2}}h_{1} : \cancel{\pi}\:\cancel{r^{2}}h_{2}}}$

$\because$ Radius and pie are equal in both the cases..

$\sf{\Rightarrow h_{1} : h_{2}}$

$\sf{\Rightarrow 12 : 18}$

$\sf{\Rightarrow \cancel{12} : \cancel{18}}$

$\sf{\Rightarrow 2 : 3}$

Hence , the ratio of volumes of the two cylinders is 2:3.......

$\blue{\Large\underline{\underline\mathtt{Extra\:Information:}}}$

• Surface area of square = $6a^{2}$
• lateral surface area of square = $4a^{2}$
• Surface area of rectangle = $2(lb + lh + bh)$
• lateral surface area of rectangle = $2h(l + b)$

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Answer 2

Answer:

$\red{\Large\underline{\underline\mathtt{Question:}}}$

Two cylinderical cans have same bases of diameter 21 cm. If one of them is 12 cm high and the other is 18 cm then, find the ratio of their volumes.

$\blue{\Large\underline{\underline\mathtt{To\:Find:}}}$

～> Ratio of the volumes of the two cylinder.

$\green{\Large\underline{\underline\mathtt{Given:}}}$

Diameter of the two cylinders = 21 cm

Height$\rightarrow h_{1} = 12 cm→h$

Height$\rightarrow h_{2} = 18 cm→h$

$\red{\Large\underline{\underline\mathtt{We\:know:}}}$

☞✧Volume of the Cylinder ✧

$\purple{\sf{\underline{\boxed{V_{c} = \pi\:r^{2}h}}}}$

$\blue{\Large\underline{\underline\mathtt{Concept:}}}$

In this case , by comparing the two volumes of the given cylinder we can find the ratio of there volumes......

$\green{\Large\underline{\underline\mathtt{Solution:}}}$

By comparing the two volumes, we get

$\purple{\sf{V_{1} : V_{2}}}$

$\purple{\sf{\pi\:r^{2}h_{1} : \pi\:r^{2}h_{2}}}$

$\purple{\sf{\cancel{\pi}\:\cancel{r^{2}}h_{1} : \cancel{\pi}\:\cancel{r^{2}}h_{2}}}$

$\because$∵ Radius and pie are equal in both the cases..

$\sf{\Rightarrow h_{1} : h_{2}}$

$\sf{\Rightarrow 12 : 18}$

$\sf{\Rightarrow \cancel{12} : \cancel{18}}$

$\sf{\Rightarrow 2 : 3}$

Hence , the ratio of volumes of the two cylinders is 2:3.......

$\blue{\Large\underline{\underline\mathtt{Extra\:Information:}}}$

Surface area of square = 6a^{2}6a

lateral surface area of square = 4a^{2}4a

Surface area of rectangle = 2(lb + lh + bh)2(lb+lh+bh)

lateral surface area of rectangle = 2h(l + b)2h(l+b)

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