Question

Calcule o volume de cada cone reto.

Answer 1

Boa noite!

a)

$v = \frac{\pi \times {r}^{2} \times h}{3} \\ \\ v = \frac{3.14 \times {4}^{2} \times 15 }{3} \\ \\ v = \frac{753.6}{3} = 251.2 \: {cm}^{3}$



b)

${30}^{2} = {12}^{2} + {x}^{2} \\ 900 = 144 + {x}^{2} \\ { - x}^{2} = 144 - 900 \\ { - x}^{2} = - 756 \\ x = \sqrt{756} = 27.5 \\ \\ v = \frac{3.14 \times {12}^{2} \times 27.5 }{3} = \frac{12434}{3} = 4144 \: {cm}^{3}$




c)

${26}^{2} = {24}^{2} + {r}^{2} \\ 676 = 576 + {r}^{2} \\ { - r}^{2} = 576 - 676 \\ { - r}^{2} = - 100 \\ r = \sqrt{100} = 10$

$v = \frac{3.14 \times {10}^{2} \times 24 }{3} = \frac{7536}{3} = 2512 \: {cm}^{3}$


d)

${15}^{2} = {r}^{2} + {2r}^{2} \\ 225 = 3 {r}^{2} \\ {r}^{2} = \frac{225}{3} \\ {r}^{2} = 75 \\ r = \sqrt{75} \\ r = 8.7$

$v = \frac{3.14 \times {8.7}^{2} \times (2 \times 8.7) }{3} \\ \\ v = \frac{4135}{3} = 1378 \: {cm}^{3}$




Espero ter te ajudado! :*