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Answers
The curved surface area of cylinder pillar is 264 metre square and its volume is 924 cm³
Find the diameter and the height of pillar
As we know that
Curved surface area of cylindrical pillar
\sf 2πrh=264m^22πrh=264m
2
---(i)
Volume of cylinder pillar
\sf πr^2h=924m^3πr
2
h=924m
3
------(ii)
Divide (ii) by (i)
\implies\sf \frac{πr^2h}{2πrh}=\frac{924}{264}⟹
2πrh
πr
2
h
=
264
924
\implies\sf \frac{r}{2}=\frac{924}{264}⟹
2
r
=
264
924
\implies\sf r=\frac{2×924}{264}⟹r=
264
2×924
\implies\sf r=7m⟹r=7m
Substitute the value of r in equation (i)
\implies\sf 2πrh=264⟹2πrh=264
\implies\sf 2×\frac{22}{7}×7×h=264⟹2×
7
22
×7×h=264
\implies\sf 44h=264⟹44h=264
\implies\sf h=\cancel\frac{264}{44}=6m⟹h=
44
264
=6m
\large{\boxed{\bf{Required\:diameter=2×7=14m}}}
Requireddiameter=2×7=14m
\large{\boxed{\bf{Required\:height=6m}}}
Requiredheight=6m
Curved surface area of cylindrical pillar
\implies\sf 2πrh=264⟹2πrh=264
\implies\sf πrh=\cancel\frac{264}{2}=132m^2⟹πrh=
2
264
=132m
2
----(i)
Volume of cylindrical pillar
\implies\sf πr^2h=924⟹πr
2
h=924
we can write in this way also
\implies\sf r(πrh)=924⟹r(πrh)=924
Substitute the value of πrh from (i)
\implies\sf 132r=924⟹132r=924
\implies\sf r=\cancel\frac{924}{132}=7m⟹r=
132
924
=7m
To find the value of height , we need to substitute the value of r in equation (i)
\implies\sf πrh=132⟹πrh=132
\implies\sf \frac{22}{7}×7×h=132⟹
7
22
×7×h=132
\implies\sf h=\cancel\frac{132}{22}=6m⟹h=
22
132
=6m
\large{\boxed{\bf{Required\:diameter=2×7=14m}}}
Requireddiameter=2×7=14m
\large{\boxed{\bf{Required\:height=6m}}}
Requiredheight=6m
★Curved surface area of cylinder★
= 2πrh
★Volume of cylinder ★
= πr²h
★Total surface area of cylinder★
= 2πrh+2πr²
Hope it helps u
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