Question

The curved surface area of a cylinder is 264 m² and its volume is 924 m³. The ratio of its diameter to its height is
(a)3 : 7
(b)7 : 3
(c)6 : 7
(d)7 : 6

Answer 1

Answer:

The Ratio of its diameter to its Height is 7 : 3 .

Among the given options option (b) 7 : 3  is the correct answer.

Step-by-step explanation:

Given :  

Curved surface area of a cylinder , C.S.A = 264 cm²

Volume of the cylinder ,V = 924 cm³

 

C.S.A of a cylinder = 264 cm²

2πrh = 264 cm²

rh = 264/2π

rh = 264 / 2× 22/7

rh = (264 × 7)/(44)

rh = 6 × 7  

rh = 42 cm …………..(1)

 

Volume of the cylinder ,V = 924 cm³

πr²h = 924 cm³

πr(rh) = 924 cm³

22/7 × r × 42 = 924  

[From eq 1]

22r × 6 = 924

132r = 924

r = 924/132

r = 7 cm

Radius of the cylinder = 7 cm  

 

On putting the value of r = 7 cm in eq 1  

rh = 42 cm

7 × h = 42

h = 42/7

h = 6 cm

Height of a Cylinder =  6 cm  

 

Diameter of a Cylinder , d = 2 × Radius  

d = 2 × 7  

d = 14 cm

Diameter of a Cylinder = 14 cm

Ratio of its diameter to its Height = d : h  

d : h = 14 : 6  

d : h = 7 : 3  

Hence, the Ratio of its diameter to its Height is 7 : 3 .

HOPE THIS ANSWER WILL HELP YOU…

 

Answer 2

Answer:

The ratio of the diameter to its height = 7 : 3

Among the given option, Option $<b><u>b) 7 : 3</u></b>$

Step-by-step explanation:

Let the radius and height of the given cylinder be r and h respectively

Volume of the cylinder = 924 m³

⇒ πr²h = 924 m³ ......... (1)

Curved Surface Area ( C.S.A ) of the cylinder = 264 m²

⇒2πrh = 264 m²

⇒πrh = 132 m² ......... ( 2 )

Dividing eq ( 1 ) by ( 2 ), we get,

$\frac{\pi \: \times \: r^{2} \: \times \: h}{\pi \: \times r \: \times \: h}$ = $\frac {924}{132}$

⇒ r = 7 m

Putting the value of r in (2), we get

π × 7 m × h = 132 m²

⇒ $\frac{22}{7}$ × 7 × h = 132 m²

⇒ 22h × 1 m = 132 m²

⇒ h = 6 m

Diameter = 2r

= 2 × 7

= 14 m

$<b><u>•°• Ratio of the diameter to its height = 14 m : 6 m = 7 : 3</u></b>$