Question

The curved surface area of a cylinder is 264m^2 and it's volume is 924m^3. find the ratio of its height to its diameter ​

Answer 1

Answer:

3:7

Step-by-step explanation:

Given,

Curved surface area of the cylinder

$= 264 {m}^{2}$

Volume of the cylinder

$= 924 {m}^{3}$

Therefore,

First Case:

According to the problem,

$= > \frac{\pi {r}^{2} h} {2\pi rh} = \frac{924 {m}^{3} }{264 {m}^{2} }$

$= > \frac{r}{2} = \frac{7}{2}$

$= > r = \frac{7}{2} \times 2$

$= > r = 7$

Hence we got,

Diameter of the cylinder = r × 2 = 7m × 2 = 14m

Second Case:

Curved surface area of the cylinder

$= {264m}^{2}$

Radius of the cylinder = 7m

Therefore,

By the problem,

$= > 2\pi rh = 264 {m}^{2}$

$= > 2 \times \frac{22}{7} \times 7 \times h = 264$

$= >2 \times 22 \times h = 264$

$= > h = \frac{264}{22 \times 2}$

=> h = 6

Hence, we got,

Height of the cylinder = 6m

Last Case:

Ratio of height to diameter

$= \frac{6}{14}$

$= \frac{3}{7}$

= 3:7

Result:

Hence required ratio of height to diameter is 3:7(Ans)

Answer 2

Solution:-

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$\implies$ Here it is given in the question that the curved surface area of a cylinder is 264 m² and it's volume is 924 m³ respectively. Now, the question has asked us to find out the ratio of its height to its diameter. To find the ratio of its height to its diameter follow the steps given below.

ANSWER:-

⌬ The ratio of its height to its diameter is 3:7.

GIVEN:-

➢ Curved Surface Area = 264 m²

➢ Volume = 924 m³

TO FIND:-

⟹ Ratio of height to diameter = ?

SOLVING STEP BY STEP:-

☯ As we know CSA of cylinder = 2πrh

➜ 2 × π × r × h = 264

➜ π × r × h = 132 m² ...(1)

☯ Volume is 924 m²

➜ π × r² × h = 924 m³ ..(2)

☯ Dividing (2) by (1)

➜ π × r² × h /π × r × h = 924 m³/132 m²

➜ r = 7 m

☯ Then, diameter is 2r = 2× 7 = 14 m

☯ From above (1) eq we know

➜ π × r × h = 132

➜ Putting r = 7

➜ 22/7 × 7 × h = 132

➜ 22 × h = 132

➜ h = 132/22

➜ H = 6 m

☯Ratio of diameter to height is H/D

➜ 6/14 = 3/7

➜ 3 : 7 is the answer

Thus, we got the answer. The ratio of its height to its diameter is 3:7.

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