A cone is 14cm deep and the base radius is 4\(\frac{1}{2}\)cm. Calculate the volume of water that is exactly half the volume of the cone.[Take \pi = \(\frac{22}{7}\)]
A
49.5cm3
B
99cm3
C
148.5cm3
D
297cm3
E
445.5cm3
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
Volume of a cone = \(\frac{1}{3} \pi r^2 h\)
r = 4\(\frac{1}{2}\) cm; h = 14 cm
Volume of cone = \(\frac{1}{3} \times \frac{22}{7} \times \frac{9}{2} \times \frac{9}{2} \times 14\)
= 297 cm\(^3\)
When half- filled, the volume of the water = \(\frac{297}{2} = 148.5 cm^3\)
Source: Myschool Past Questions Archive (Record #23202)