Answer
Verified
425.4k+ views
Hint: In this problem we have been provided with a cone whose height and volume are known to us, this cone is said to have an equal radii and height with that of a cylinder, so we need to find the total surface area. Simply the use of formula for volume of cones will help us find out the radii of cones as height is given to us. Use this radii in finding out the T.S.A of the cylinder.
Volume of cone, V= 753.6 $c{m^3}$(given)
Height of cone, H = 5 cm (given)
Now using the formula for volume of cone $V = \dfrac{1}{3}\pi {r^2}h$………………. (1)
Substituting the values in equation (1) we get
$
753.6 = \dfrac{1}{3}\pi {r^2}5 \\
\Rightarrow 452.16 = \pi {r^2} \\
$
Using $\pi = 3.14$ we get
$
{r^2} = 144 \\
\Rightarrow r = \pm 12 \\
$
Radius of base for a cone can’t be negative thus we will take up only positive value hence r=12 cm.
Now the formula for Total surface area of cylinder ${\text{T}}{\text{.S}}{\text{.A = 2}}\pi {{\text{r}}^2} + 2\pi rH$……………….. (2)
As the radii and the height of cone are equal to that of cylinder thus substituting the values we get
${\text{T}}{\text{.S}}{\text{.A = 2}} \times {\text{3}}{\text{.14}} \times {12^2} + 2 \times 3.14 \times 12 \times 5$
On solving we get
$T.S.A = 1218.12{\text{ c}}{{\text{m}}^2}$
Thus option (a) is the right answer for this problem.
Note: Whenever we face such types of problems the key concept is simply the formula, thus it is advisable to have a good gist of all the formula especially the area, volume, T.S.A and C.S.A for various conic sections like cone, hemisphere, cylinder etc. This will help you to reach the right answer.
Volume of cone, V= 753.6 $c{m^3}$(given)
Height of cone, H = 5 cm (given)
Now using the formula for volume of cone $V = \dfrac{1}{3}\pi {r^2}h$………………. (1)
Substituting the values in equation (1) we get
$
753.6 = \dfrac{1}{3}\pi {r^2}5 \\
\Rightarrow 452.16 = \pi {r^2} \\
$
Using $\pi = 3.14$ we get
$
{r^2} = 144 \\
\Rightarrow r = \pm 12 \\
$
Radius of base for a cone can’t be negative thus we will take up only positive value hence r=12 cm.
Now the formula for Total surface area of cylinder ${\text{T}}{\text{.S}}{\text{.A = 2}}\pi {{\text{r}}^2} + 2\pi rH$……………….. (2)
As the radii and the height of cone are equal to that of cylinder thus substituting the values we get
${\text{T}}{\text{.S}}{\text{.A = 2}} \times {\text{3}}{\text{.14}} \times {12^2} + 2 \times 3.14 \times 12 \times 5$
On solving we get
$T.S.A = 1218.12{\text{ c}}{{\text{m}}^2}$
Thus option (a) is the right answer for this problem.
Note: Whenever we face such types of problems the key concept is simply the formula, thus it is advisable to have a good gist of all the formula especially the area, volume, T.S.A and C.S.A for various conic sections like cone, hemisphere, cylinder etc. This will help you to reach the right answer.
Recently Updated Pages
Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred
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
Trending doubts
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Write an application to the principal requesting five class 10 english CBSE
Difference Between Plant Cell and Animal Cell
a Tabulate the differences in the characteristics of class 12 chemistry CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
Discuss what these phrases mean to you A a yellow wood class 9 english CBSE
List some examples of Rabi and Kharif crops class 8 biology CBSE