A metallic solid spherical ball of radius 3 cm is melted recast into three spherical balls. The radii of two of these balls are 2 cm and 1.5 cm. What is the surface area (in cm2) of the third ball?
A. 50π
B. $$\frac{{25}}{4}$$π
C. 25π
D. $$\frac{{25}}{2}$$π
Answer: Option C
Solution (By Examveda Team)
$$\frac{4}{3}$$π × 3 × 3 × 3 = $$\frac{4}{3}$$π × 23 + $$\frac{4}{3}$$π × (1.5)3 + $$\frac{4}{3}$$π × r327 = 8 + 3.375 + r3
15.625 = r3
r = 2.5 cm
∴ The surface area of the third ball = 4π × 2.5 × 2.5 = 25π cm2
This Question Belongs to Arithmetic Ability >> Mensuration 3D
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A sphere and a hemisphere have the same volume. The ratio of their curved surface area is:
A. $${2^{\frac{3}{2}}}:1$$
B. $${2^{\frac{2}{3}}}:1$$
C. $${4^{\frac{2}{3}}}:1$$
D. $${2^{\frac{1}{3}}}:1$$
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