Question

Courses
The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924 m. Find the ratio of its diameter to its
height
Select one:
. a.4:5
b.3:7
c. 5:4

d. 7:3
​

Answer 1

Answer ::

The ratio between the diameter of cylinder to it's height of cylinder is 7:3 [ Option. d. ] is correct.

Step-by-step explanation ::

To Find :-

• The ratio of the diameter to it's height of cylinder

Solution :-

Given that,

• Curved surface area of cylinder = 264m²
• Volume of Cylinder = 924m²

As we know that,

• Curved surface area of cylinder = 2πrh . . . . ( ii )

• Volume of Cylinder = πr²h . . . ( i )

On dividing ( ii ) by ( i ),

$\sf{\mapsto \: \dfrac{\pi \: {r}^{2}h}{2 \: \pi \: rh} = \dfrac{924}{264}} \\ \\ \\ \sf{\mapsto \: \dfrac{\cancel{{\pi \: r}^{2}h}}{2 \: \cancel{\pi \: rh}} = \dfrac{924}{264}} \\ \\ \\ \sf{\mapsto \: \dfrac{r}{2} = \dfrac{924}{264}} \\ \\ \\ \sf{\mapsto \: r = \: \dfrac{924 \times 2}{264}} \\ \\ \\ \sf{\mapsto \: r = \dfrac{1848}{264}} \\ \\ \\ \sf{\mapsto \: r = \cancel{\dfrac{1848}{264}}} \\ \\ \\ \bf{\mapsto \: r = 7}$

Therefore the diameter is,

As we know that,

Diameter = 2 × Radius

= 2 × 7

= 14m

Now, height. By putting r = 7, in ( i ),

Let us assume the height as h metres.

$\sf{ \mapsto \: 2 \times \dfrac{22}{7} \times 7 \times h = 264} \\ \\ \\ \sf{ \mapsto \: 2 \times \dfrac{22}{ \cancel{7}} \times \cancel{7} \times h = 264} \\ \\ \\ \sf{ \mapsto \: 2 \times 22 \times h = 264} \\ \\ \\ \sf{ \mapsto \: 44 \times h = 264} \\ \\ \\ \sf{ \mapsto \: h = \dfrac{264}{44}} \\ \\ \\ \sf{ \mapsto \: h = \cancel{ \dfrac{264}{44}}} \\ \\ \\ \bf{ \mapsto \: h = 6}$

Therefore, the height of cylinder is 6m.

ACCORDING THE QUESTION,

The ratio of diameter is to it's height is,

$\sf{\mapsto \: Diameter : Height} \\ \\ \\ \sf{\mapsto \: 14 : 6} \\ \\ \\ \sf{\blue{\mapsto \: 7 : 3} \: \: \: \: \: \dag}$

Hence, the ratio between the diameter to it's height is 7:3.

Answer 2

☆Given Question :-

• The curved surface area of a cylindrical pillar is 264 m^2 and its volume is 924 m^3. Find the ratio of its diameter to its height.

____________________________________________

$\huge \orange{AηsωeR}$

☆Given :-

• The curved surface area of a cylindrical pillar is 264 m^2 Volume of cylindrical pillar is 924 m^3.

☆To Find :-

• The ratio of its diameter to its height.

☆Formula used :-

${{ \boxed{\large{\bold\green{Curved Surface Area_{(Cylinder)}\: = \:2\pi rh}}}}}$

${{ \boxed{\large{\bold\red{Volume_{(Cylinder)}\: = \:\pi r^2 h }}}}}$

where,

• r = radius of cylinder
• h = height of cylinder

$\begin{gathered}\Large{\bold{{\underline{CaLcUlAtIoN\::}}}} \end{gathered}$

$\begin{gathered}\begin{gathered}\bf Let = \begin{cases} &\sf{r \: be \: the \: radius \: of \: cylinder} \\ &\sf{h \: be \: the \: height \: of \: cylinder} \end{cases}\end{gathered}\end{gathered}$

$\sf \: ⟼According \: to \: statement$

$\sf \: Curved \: Surface \: Area = 264 \: {m}^{2}$

$\sf \: ⟼2\pi \: rh = 264 \: ⟼ \: (1)$

$\large \red{\sf \:  ⟼ According \: to \: statement}$

$\sf \: Volume = 924 \: {m}^{3}$

$\sf \: ⟼\pi \: {r}^{2} h = 924 \: ⟼ \: (2)$

☆ On dividing equation (2) by equation (1), we get

$\sf \: \dfrac{\pi \: {r}^{2} h}{2\pi \:rh} = \dfrac{924}{264}$

$\sf \: ⟼\dfrac{r}{2} = \dfrac{7}{2}$

$\bf\implies \:r = 7\: m \: ⟼ \: (3)$

☆ On substituting r = 7, in equation (1), we get

$\sf \: ⟼2 \times \dfrac{22}{7} \times 7 \times h = 264$

$\bf\implies \:h \: = 6 \: m$

☆ Now, we have to find ratio of its diameter to its height.

$\bf \:  Diameter: height$

$\bf\implies \:2r : h$

$\bf\implies \:2 \times 7: 6$

$\bf\implies \:7 : 3$

$\large{\boxed{\boxed{\bf{Option \: (d) \: is \: correct}}}}$

___________________________________________

☆ More information:-

Perimeter of rectangle = 2(length× breadth)

Diagonal of rectangle = √(length)²+ (breadth)²)

Area of square = side²

Perimeter of square = 4× side

Volume of cylinder = πr²h

T.S.A of cylinder = 2πrh + 2πr²

Volume of cone = ⅓ πr²h

C.S.A of cone = πrl

T.S.A of cone = πrl + πr²

Volume of cuboid = l × b × h

C.S.A of cuboid = 2(l + b)h

T.S.A of cuboid = 2(lb + bh + lh)

C.S.A of cube = 4a²

T.S.A of cube = 6a²

Volume of cube = a³

Volume of sphere = 4/3πr³

Surface area of sphere = 4πr²

Volume of hemisphere = ⅔ πr³

C.S.A of hemisphere = 2πr²

T.S.A of hemisphere = 3πr²

__________________________________________