Question

17. What is the ratio of the volume of a cylinder and that of a cone on the same base and of the same height?
(1) 1:2
(2) 1:4
(3) 4:3
(4) 3:1​

Answer 1

Answer:

Ratio = Volume of cylinder/ Volume of cone

= πr^2h/ 1/3πr^2h

= 1÷1/3

= 3/1

Therefore option 4 is correct

Answer 2

Answer :-

Volume of cylinder = πr²h

Volume of cone = ⅓ πr²h

Ratio of volume of cylinder to volume of cone = πr²h : ⅓ πr²h

= 3 πr²h : πr²h

= 3 : 1

The ratio of the volume of a cylinder and that of a cone = 3 : 1

$\boxed{\begin{minipage}{6.2 cm}\bigstar \:\underline{\textbf{Formulae Related to Cylinder :}}\\\\\sf {\textcircled{\footnotesize\textsf{1}}} \:Area\:of\:Base\:and\:top =\pi r^2 \\\\ \sf {\textcircled{\footnotesize\textsf{2}}} \:\:Curved \: Surface \: Area =2 \pi rh\\\\\sf{\textcircled{\footnotesize\textsf{3}}} \:\:Total \: Surface \: Area = 2 \pi r(h + r)\\ \\{\textcircled{\footnotesize\textsf{4}}} \: \:Volume=\pi r^2h\end{minipage}}$

$\boxed{\begin{minipage}{6 cm}\bigstar \:\underline{\textbf{Formulae Related to Cone :}}\\\\\sf {\textcircled{\footnotesize\textsf{1}}} \:Area\:of\:Base =\pi r^2 \\\\ \sf {\textcircled{\footnotesize\textsf{2}}} \:\:Curved \: Surface \: Area = \pi rl\\\\\sf{\textcircled{\footnotesize\textsf{3}}} \:\:TSA = Area\:of\:Base + CSA=\pi r^2+\pi rl\\ \\{\textcircled{\footnotesize\textsf{4}}} \: \:Volume=\dfrac{1}{3}\pi r^2h\\ \\{\textcircled{\footnotesize\textsf{5}}} \: \:Slant \: Height=\sqrt{r^2 + h^2}\end{minipage}}$