Question

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

Answer 1

$\huge \underline \mathsf \red {SOLUTION:-}$

Given That:

• Curved surface area of cylinder = 264 m²
• Volume of cylinder = 924 m³

We know that,

• CSA of cylinder = 2πrh

So,

➠ 264 = 2 × 22/7 × r × h

➠ r × h = (264 × 7)/44

➠ r × h = 1848/44

➠ r × h = 42

➠ h = 42/r ……(1)

Now,

• volume of cylinder = πr²h

Substituting the value of h = 42/r in the volume equation, we get

➠ 924 = 22/7 × r² × 42/r

➠ 924r = 924 × 7

➠ r = 7 m

So,

Radius is 7 m and the diameter will be

= 7 × 2

= 14 m.

And the height of the cylinder

= h = 42/r

= 42/7

= 6 m

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Answer 2

Given,

curved surface area

of cylindrical pillar. = 264m^2

Volume = 924^3

We know that ,

C.S.A of cylinder = 2πrh

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

$rh = 264 \times 7 \times \frac{22}{2}$

$rh = 42$

h= 42r ---------> 1⃣

Volume of the cylinder = πr^2h

$924 = \frac{22}{7} \times {r}^{2} \times 42r$

$r = \frac{924 \times 7}{22 \times 42}$

r=7m

we know that

d=2r = 2×7 =14m

from equation 1⃣

h =42/r

$\frac{42}{7}$

=6

so,the answer is

diameter = 14m and height = 6m