# The volume of a cone of height 5 cm is 753.6 $c{m^3}$.Thus cone and a cylinder have equal radii and height. Find the total surface area of the cylinder. (Given$\pi = 3.14$).

$

(a){\text{ 1281}}{\text{.12 c}}{{\text{m}}^2} \\

(b){\text{ 1589}}{\text{.12 c}}{{\text{m}}^2} \\

(c){\text{ 1242}}{\text{.12 c}}{{\text{m}}^2} \\

(d){\text{ 1527}}{\text{.12 c}}{{\text{m}}^2} \\

$

Last updated date: 21st Mar 2023

•

Total views: 306.9k

•

Views today: 5.85k

Answer

Verified

306.9k+ 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

If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE