The truck of a tree is a right cylinder 1.5 m in radius and 10 m high. The volume of the timber which remains when the truck is trimmed just enough to reduce it to a rectangular parallelopiped on a square base is :
A. 44 m3
B. 45 m3
C. 46 m3
D. 47 m3
Answer: Option A
Solution(By Examveda Team)
Let the length of each side of the square base be x metres
Then,
$$\eqalign{ & {x^2} + {x^2} = {\left( 3 \right)^2} \cr & \Rightarrow 2{x^2} = 9 \cr & \Rightarrow {x^2} = \frac{9}{2} \cr & \Rightarrow x = \frac{3}{{\sqrt 2 }} \cr} $$
∴ Volume of parallelopiped :
$$\eqalign{ & = \left( {\frac{3}{{\sqrt 2 }} \times \frac{3}{{\sqrt 2 }} \times 10} \right){{\text{m}}^{\text{3}}} \cr & = \frac{{90}}{2}{{\text{m}}^{\text{3}}} \cr & = 45\,{{\text{m}}^{\text{3}}} \cr} $$
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
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