Question

The curved surface area of a cylindrical pillar is 264 m² and its volume is 924 m³.Find the diameter and the height of the pillar.​

Answer 1

Step-by-step explanation:

CSA of cylinder =2 pie×r×h = 264

=pie × r × h=264/2=132

volume of cylinder =pie × r ^2 ×h = 924

=pie×r×r×h=924

=132×r=924

r=924/132 = 7

diameter = 2×7 =14m

pie × r × h = 132

22/7 ×7 × h=132

22×h =132

height h =132/22=6m

Answer 2

${\pmb{\underline{\sf{ Required \ Solution ... }}}}$

• Curved surface area of a cylindrical pillar is 264 m²
• Volume is 924 m³

Let the Radius and Height of the Cylinder be r and h Respectively.

$\\ {\pmb{\underline{\sf{ Formulation ... }}}}$

$\colon\implies{\sf\large{ \left( Curved \ Surface \ Area_{(Cylinder )} = 2πrh \right) }} \\ \\ \colon\implies{\sf{ \cancel{264} = \cancel{2} πrh }} \\ \\ \colon\implies{\sf{ 132 = \dfrac{22}{7} rh }} \\ \\ \colon\implies{\sf{ \dfrac{ \cancel{132} \times 7}{ \cancel{22} } = rh }} \\ \\ \colon\implies{\sf{ 6 \times 7 = rh }} \\ \\ \colon\implies{\sf{ r \times h = 42 \ m \ \ \ \ \ \cdots(1) }}$

Now, We have to Volume of the Cylinder Formula as to get:

$\colon\implies{\sf\large{ \left( Volume_{(Cylinder )} = πr^2h \right) }} \\ \\ \colon\implies{\sf{ 924 = πr^2h }} \\ \\ \colon\implies{\sf{ \dfrac{ \cancel{924} \times 7}{ \cancel{22} } = r^2h }} \\ \\ \colon\implies{\sf{ 21 \times 7 = r^2h }} \\ \\ \colon\implies{\sf{ 147 = r \times r \times h }} \\ \\ \colon\implies{\sf{ 147 = r \times 42 }} \\ \\ \colon\implies{\sf{ \cancel{ \dfrac{147}{42} } = r }} \\ \\ \colon\implies{\sf{ r = \dfrac{21}{6} }} \\ \\ \colon\implies{\sf{ r = \dfrac{7}{2} m }}$

So, The Diameter of the Cylinder will be as:

$\colon\implies{\sf{ D = 2r }} \\ \\ \colon\implies{\sf{D = \cancel{2} \times \dfrac{7}{ \cancel{2} } }} \\ \\ \colon\implies{\underline{\boxed{\sf{ D = 7 \ m }}}}$

$\\ {\pmb{\underline{\sf{Value \ Substitution ... }}}}$

Now, It's time to find the Height of the Cylindrical Pillar by applying Got value into Eq. (1) as:-

$\colon\implies{\sf{ r \times h = 42 }} \\ \\ \colon\implies{\sf{ \dfrac{7}{2} \times h = 42 }} \\ \\ \colon\implies{\sf{ h = \dfrac{ \cancel{42} \times 2}{ \cancel{7} } }} \\ \\ \colon\implies{\sf{ h = 6 \times 2 }} \\ \\ \colon\implies{\underline{\boxed{\sf{ 12 \ m_{(Height)} }}}}$

Hence,

• Diameter of the Cylinder = 7 m
• Height of the Cylinder = 12 m