A right circular cone and a right circular cylinder have equal base and equal height. If the radius of the base and the height are in the ratio 5 : 12, then the ratio of the total surface area of the cylinder to that of the cone is :
A. 3 : 1
B. 13 : 9
C. 17 : 9
D. 34 : 9
Answer: Option C
Solution(By Examveda Team)
Let their radius and height be 5x and 12x respectivelySlant height of the cone,
$$l = \sqrt {{{\left( {5x} \right)}^2} + {{\left( {12x} \right)}^2}} = 13x$$
$$\eqalign{ & \frac{{{\text{Total surface area of cylinder}}}}{{{\text{Total surface area of cone}}}} \cr & = \frac{{2\pi r\left( {h + r} \right)}}{{\pi r\left( {l + r} \right)}} \cr & = \frac{{2\left( {h + r} \right)}}{{\left( {l + r} \right)}} \cr & = \frac{{2 \times \left( {12x + 5x} \right)}}{{\left( {13x + 5x} \right)}} \cr & = \frac{{34x}}{{18x}} \cr & = \frac{{17}}{9}\,Or\,17:9 \cr} $$
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
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