Question

The ratio of height of two cylinders is 5:3, as well as the ratio of their
radii is 2:3. Find the ratio of the volumes of the cylinders.
the area of canyas required for a conical tent of height 24m and​

Answer 1

Given :

• Ratio of the height of the two cylinders = 5 : 3
• Ratio of the radii of the two cylinders = 2 : 3

To find :

• Ratio of the volumes of the two cylinders.

Concept :

→ Formula to calculate volume of cylinder :-

• Volume of cylinder = πr²h

Where,

• Take π = 22/7
• r = radius
• h = height

Solution :

Let,

• Height of the first cylinder = 5h
• Height of the second cylinder = 3h
• Radius of the first cylinder = 2r
• Radius of the second cylinder = 3r

Volume of first cylinder :-

$\\ \dashrightarrow \quad \sf Volume = \pi {r}^{2} h$

$\\ \dashrightarrow \quad \sf Volume = \pi \times {(2r})^{2} \times 5h$

$\\ \dashrightarrow \quad \sf Volume = \pi \times {4r}^{2} \times 5h$

$\\ \dashrightarrow \quad \sf Volume = \pi \times 20 {r}^{2}h$

• Volume of the first cylinder = 20r²h × π

Volume of second cylinder :-

$\\ \dashrightarrow \quad \sf Volume = \pi {r}^{2} h$

$\\ \dashrightarrow \quad \sf Volume = \pi {(3r})^{2} \times 3 h$

$\\ \dashrightarrow \quad \sf Volume = \pi \times {9r}^{2} \times 3 h$

$\\ \dashrightarrow \quad \sf Volume = \pi \times {27r}^{2}h$

• Volume of the second cylinder = 27r²h × π

$\\ \dashrightarrow \quad \rm Ratio = \dfrac{Volume \: of \: first \: cylinder}{Volume \: of \: second \: cylinder}$

$\\ \dashrightarrow \quad \sf Ratio = \dfrac{20 {r}^{2}h \times \pi }{27 {r}^{2}h \times \pi }$

$\\ \dashrightarrow \quad \sf Ratio = \dfrac{20 \not{r}^{2} \not h \times \not\pi }{27 \not{r}^{2} \not h \times \not\pi }$

$\\ \dashrightarrow \quad \sf Ratio = \dfrac{20}{27}$

• Ratio of the volumes of the two cylinders = 20 : 27