Question

Uma esfera apresenta raio igual a 5 cm. Determine;

a)A área da superfície esférica
b)O volume

Answer 1

$\boxed{A = 4 \cdot \pi \cdot R^{2}}$

$\boxed{V = \frac{4 \cdot \pi \cdot R^{3}}{3}}$

Substituindo:

a)
$A = 4 \cdot \pi \cdot R^{2} \\\\ A = 4 \cdot \pi \cdot (5)^{2} \\\\ A = 4 \cdot \pi \cdot 25 \\\\ \boxed{\boxed{A = 100\pi \ cm^{2}}}$

b)
$V = \frac{4 \cdot \pi \cdot R^{3}}{3} \\\\ V = \frac{4 \cdot \pi \cdot (5)^{3}}{3} \\\\ V = \frac{4 \cdot \pi \cdot 125}{3} \\\\ V = \frac{500\pi}{3} \\\\ \boxed{\boxed{V = \frac{500}{3}\pi \ cm^{3}}}$

Answer 2

a)

$A = 4* \pi * r^2 \\ \\ \\ A = 4 * 5^2 * \pi \\ \\ \\ A = 4*25* \pi \\ \\ \\ A = 100* \pi \ cm^2$

==========

b)

$V = \dfrac{4}{3}* \pi *r^3 \\ \\ \\ V = \dfrac{4}{3} * 5^3 * \pi \\ \\ \\ V = \dfrac{4}{3} * 125 * \pi \\ \\ \\ V = \dfrac{4*125}{3} * \pi \\ \\ \\ V = \dfrac{500}{3} * \pi \\ \\ \\ V \approx 166,66 * \pi \ cm^3$