A cone of height 15 cm and base diameter 30 cm is carved out of a wooden sphere of radius 15 cm. The percentage of wood wasted is :
A. 25%
B. 40%
C. 50%
D. 75%
Answer: Option D
Solution(By Examveda Team)
Volume of sphere :$$ = \left( {\frac{4}{3}\pi \times 15 \times 15 \times 15} \right)c{m^3}$$
Volume of cone :
$$ = \left( {\frac{1}{3}\pi \times 15 \times 15 \times 15} \right)c{m^3}$$
Volume of wood wasted :
$$\eqalign{ & = \left[ {\left( {\frac{4}{3}\pi \times 15 \times 15 \times 15} \right) - \left( {\frac{1}{3}\pi \times 15 \times 15 \times 15} \right)} \right] \cr & = \left( {\pi \times 15 \times 15 \times 15} \right) \cr} $$
∴ Required percentage :
$$\eqalign{ & = \left( {\frac{{\pi \times 15 \times 15 \times 15}}{{\frac{4}{3}\pi \times 15 \times 15 \times 15}}} \right)\% \cr & = 75\% \cr} $$
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