Question

12 spheres of the same size are made from melting a solid cylinder of 16 cm diameter
and 2 cm height. The diameter of each sphere is
(a) 13 cm
(b) 2 cm
(c) 3 cm
(d) 4 cm​

Answer 1

Answer:

(b) 2 cm

Step-by-step explanation:

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Answer 2

$volume \: of \: the \: sphere \: = \frac{4}{3} \pi {r}^{3} \\ volume \: of \: cylinder \: = \pi {r}^{2} h \\ volume \: of \: cylinder = 12 \times volume of \: the \: sphere \: \\ \pi {r}^{2} h \: = 12 \times \frac{4}{3} \pi {r}^{3} \\ {r}^{2} h = 16 {r}^{3} \\ {8}^{2} \times 2 = 16 \times {r}^{3} \\ \frac{128}{16} = {r}^{3} \\ 8 = {r}^{3} \\ therefore \: r = \sqrt[3]{8} \\ r = 2 \: cm \: \\ diameter = 2 + 2 = 4cm$