Question

5. Find the radius of each of the following spheres with
the given surface area.
(a) 210 cm
(b) 7230 mm
(c) 3163 m
(d) 647 cm
(e) 91170 mm
(1) 49,0 m​

Answer 1

Using formula

$A = 4 \times \pi \: r {}^{2}$

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1) 210 cm²

$210 = 4 \times \frac{22}{7} \times r {}^{2} \\ \frac{210}{4} = \frac{22}{7} \times r {}^{2} \: \: \: \: \: \: \: \\ r {}^{2} = \frac{210 \times 7}{4 \times 22} \: \: \: \: \: \: \: \\ r {}^{2} = \frac{1470}{88} \: \: \: \: \: \: \: \: \: \: \: \: \\ r {}^{2} = 16.70 \: \: \: \: \: \: \: \: \: \: \: \:$

Taking square root

$r = 4.08$

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2) 7230 mm²

$7230 = 4 \times \frac{22}{7} \times r {}^{2} \\ \frac{7230}{4} = \frac{22}{7} \times r {}^{2} \: \: \: \: \: \: \\ r {}^{2} = \frac{7230 \times 7}{4 \times 22} \: \: \: \: \: \: \: \\ r {}^{2} = \frac{50610}{88} \: \: \: \: \: \: \: \: \: \: \: \: \: \\ r {}^{2} = 575.11 \: \: \: \: \: \: \: \: \: \: \:$

Taking square root

$r = 23.98$

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3) 3163mm²

$3163 = 4 \times 3.14 \times r {}^{2} \\ \frac{3163}{4 \times 3.14} = r {}^{2} \: \: \: \: \: \: \: \: \: \: \: \\ r {}^{2} = \frac{3163}{12.56} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ r {}^{2} = 251.83 \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Taking square root

$r = 15.86$

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4) 647cm²

$647 = 4 \times 3.14 \times r {}^{2} \\ r {}^{2} = \frac{647}{4 \times 3.14} \: \: \: \: \: \: \: \: \\ r {}^{2} = \frac{647}{12.56} \: \: \: \: \: \: \: \: \: \: \: \: \: \\ r {}^{2} = 51.51 \: \: \: \: \: \: \: \: \: \: \: \: \:$

Taking square root

$r = 7.17$

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5) 91170mm²

$91170 = 4 \times 3.14 \times \: r {}^{2} \\ 91170 = 12.56 \times r {}^{2} \: \: \: \: \: \: \\ r {}^{2} = \frac{91170}{12.56} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ r {}^{2} = 7258.75 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Taking square root

$r = 85.19$

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6) 490m

$490 = 4 \times 3.14 \times r {}^{2} \\ 490 = 12.56 \times r {}^{2} \: \: \: \: \\ r {}^{2} = \frac{490}{12.56} \: \: \: \: \: \: \: \: \: \: \: \: \: \\ r {}^{2} = 39.01 \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Taking square root

$r = 6.24$

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