Answer
Verified
394.2k+ views
Hint: The lateral surface area of cylinder $ = 2\pi {\text{rh}}$ where r is the radius of cylinder and h is height of the cylinder and the curved surface of cone $ = \pi {\text{Rl}}$ where R is the radius of cone and l is slant height of cone. According to the question, both are equal and the radius of both shapes are also same. Put the given values and find the ratio.
Complete step by step answer:
Given, the lateral surface of a cylinder is equal to the curved surface of a cone. The radius of the cylinder is equal to the radius of the cone. We have to find the ratio of the height of the cylinder and the slant height of the cone. We know that the lateral surface area of cylinder$ = 2\pi {\text{rh}}$where r= the radius of cylinder and h= height of cylinder. Also, the curved surface area of cone$ = \pi {\text{Rl}}$where R=radius of the cone and l- slant height of the cone. Here, given r=R and according to question,
The lateral surface area of a cylinder= the curved surface area of the cone
On putting the given values we get,
$
\Rightarrow 2\pi {\text{rh = }}\pi {\text{rl}} \\
\\
$
On simplifying we get,
$ \Rightarrow \dfrac{{\text{h}}}{{\text{l}}} = \dfrac{{\pi {\text{r}}}}{{2\pi {\text{r}}}} = \dfrac{1}{2}$
Hence the correct answer is ‘C’.
Note: The lateral surface area of a cylinder is the area of all sides of the cylinder excluding the area of its base and top. The curved surface area of the cone is the area of cone excluding the area of circle present in the cone. It is also called the lateral area. Here the student may get confused and could use the formula of total surface area of cylinder and total surface area of cone which are- $2\pi {\text{r}}\left( {{\text{h + r}}} \right)$ and $(\pi {\text{rl + }}\pi {{\text{r}}^2})$ respectively where the variables have usual meaning. But we are asked but the lateral surface, not the total surface.
Complete step by step answer:
Given, the lateral surface of a cylinder is equal to the curved surface of a cone. The radius of the cylinder is equal to the radius of the cone. We have to find the ratio of the height of the cylinder and the slant height of the cone. We know that the lateral surface area of cylinder$ = 2\pi {\text{rh}}$where r= the radius of cylinder and h= height of cylinder. Also, the curved surface area of cone$ = \pi {\text{Rl}}$where R=radius of the cone and l- slant height of the cone. Here, given r=R and according to question,
The lateral surface area of a cylinder= the curved surface area of the cone
On putting the given values we get,
$
\Rightarrow 2\pi {\text{rh = }}\pi {\text{rl}} \\
\\
$
On simplifying we get,
$ \Rightarrow \dfrac{{\text{h}}}{{\text{l}}} = \dfrac{{\pi {\text{r}}}}{{2\pi {\text{r}}}} = \dfrac{1}{2}$
Hence the correct answer is ‘C’.
Note: The lateral surface area of a cylinder is the area of all sides of the cylinder excluding the area of its base and top. The curved surface area of the cone is the area of cone excluding the area of circle present in the cone. It is also called the lateral area. Here the student may get confused and could use the formula of total surface area of cylinder and total surface area of cone which are- $2\pi {\text{r}}\left( {{\text{h + r}}} \right)$ and $(\pi {\text{rl + }}\pi {{\text{r}}^2})$ respectively where the variables have usual meaning. But we are asked but the lateral surface, not the total surface.
Recently Updated Pages
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Find the values of other five trigonometric functions class 10 maths CBSE
Trending doubts
Assertion CNG is a better fuel than petrol Reason It class 11 chemistry CBSE
How does pressure exerted by solid and a fluid differ class 8 physics CBSE
Number of valence electrons in Chlorine ion are a 16 class 11 chemistry CBSE
What are agricultural practices? Define
What does CNG stand for and why is it considered to class 10 chemistry CBSE
The rate of evaporation depends on a Surface area b class 9 chemistry CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
State whether the following statement is true or false class 11 physics CBSE
A night bird owl can see very well in the night but class 12 physics CBSE