The radius of a cylinder is 5 m more than its height. If the curved surface area of the cylinder is 792 m2, what is the volume of the cylinder ?
A. 5712 m3
B. 5244 m3
C. 5544 m3
D. 5306 m3
E. 5462 m3
Answer: Option C
Solution(By Examveda Team)
Let the height of the cylinder be x cmThen, radius = (x + 5) m
Curved surface area of the cylinder = $$2\pi rh$$
Now,
$$\eqalign{ & 2\pi \left( {x + 5} \right) \times x = 792 \cr & \Rightarrow 2 \times \frac{{22}}{7} \times \left( {{x^2} + 5x} \right) = 792 \cr & \Rightarrow {x^2} + 5x = \frac{{792 \times 7}}{{44}} = 126 \cr & \Rightarrow {x^2} + 5x - 126 = 0 \cr & \Rightarrow {x^2} + 14x - 9x - 126 = 0 \cr & \Rightarrow x\left( {x + 14} \right) - 9\left( {x + 14} \right) = 0 \cr & \Rightarrow \left( {x - 9} \right)\left( {x + 14} \right) = 0 \cr & \therefore x = 9, - 14{\text{(neglect negative value)}} \cr} $$
∴ Height of cylinder = 9 m
∴ Radius of cylinder = 9 + 5 = 14 m
Volume of cylinder :
$$\eqalign{ & = \pi {r^2}h \cr & = \frac{{22}}{7} \times 14 \times 14 \times 9 \cr & = 5544\,{m^3} \cr} $$
Related Questions on Volume and Surface Area
A. 12$$\pi$$ cm3
B. 15$$\pi$$ cm3
C. 16$$\pi$$ cm3
D. 20$$\pi$$ cm3
In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:
A. 75 cu. m
B. 750 cu. m
C. 7500 cu. m
D. 75000 cu. m
A. 84 meters
B. 90 meters
C. 168 meters
D. 336 meters
Join The Discussion