A hemisphere and a cone have equal bases. If their heights are also equal, then the ratio of their curved surface will be :
A. $$\sqrt 2 :1$$
B. $$1:\sqrt 2 $$
C. 2 : 1
D. 1 : 2
Answer: Option A
Solution(By Examveda Team)
Let,
$$\eqalign{ & OP = OQ = OR = r \cr & \therefore OR = h = r \cr} $$
∴ Curved surface area of the hemisphere = $$2\pi {r^2}$$
Curved surface area of a cone = $$\pi rl$$
Where,
$$\eqalign{ & l = \sqrt {{h^2} + {r^2}} \cr & \,\,\,\,\, = \sqrt {{r^2} + {r^2}} \cr & \,\,\,\,\, = r\sqrt 2 \cr} $$
∴ Required ratio :
$$\eqalign{ & = \frac{{2\pi {r^2}}}{{\pi rl}} \cr & = \frac{{2\pi {r^2}}}{{\pi r \times r\sqrt 2 }} \cr & = \frac{2}{{\sqrt 2 }} \cr & = \frac{{2 \times \sqrt 2 }}{{\sqrt 2 \times \sqrt 2 }} \cr & = \frac{{2\sqrt 2 }}{2} \cr & = \frac{{\sqrt 2 }}{1}\,Or\,\sqrt 2 :1 \cr} $$
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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