Question

ASAP!! ITS URGENT

Find the lateral area, total area, and volume of each right circular come.

Answer 1

58.

`135\pi \: {km}^(2)`

59.

`216\pi \: {km}^(2)`

60.

`324 \: {km}^(3)`

61.

`72 √(5 ) \pi \: {m}^(2)`

62.

`72( √(5) + 2)\pi \: {m}^(2)`

63.

`240\pi \: {m}^(3)`

Explanation:

58. First, we have to find the length of the cone shaper by using the Pythagorean theorem:

`{l}^(2) = {12}^(2) + {9}^(2) = 144 + 81 = 225`

`l > 0`

`l = √(225) = 15 \: km`

Now, let's find the lateral surface (r = 9 km):

`a(lateral) = \pi * r * l = \pi * 9 * 15 = 135\pi \: {km}^(2)`

59. The area of total surface is equal to a lateral surface's and base surface's sum:

Let's find the area of the base first:

`a(base) = \pi * {r}^(2) = {9}^(2) * \pi = 81\pi \: {km}^(2)`

Now, let's find the area of total surface:

`a(total) = 135\pi + 81\pi = 216\pi\: {km}^(2)`

60. h = 12 km

`v = (1)/(3) * a(base) * h = (1)/(3) * 81\pi * 12 = 324\pi \: {km}^(3)`

61. r = 12m

h = 5m

Let's find the length of the cone shaper by using the Pythagorean theorem:

`{l}^(2) = {12}^(2) + {6}^(2) = 144 + 36 = 180`

`l > 0`

`l = √(180) = 6 √(5) \: m`

Now, let's find the area of the lateral surface:

`a(lateral) = \pi * r * l = \pi * 12 * 6 √(5) = 72 √(5) \pi \: {m}^(2)`

62.

`a(base) = \pi * {r}^(2) = 144\pi \: {m}^(2)`

`a(total) = 72 √(5) \pi + 144\pi = 72( √(5) + 2)\pi \: {m}^(2)`

63.

`v = (1)/(3) * a(base) * h = (1)/(3) * 144\pi * 5 = 240\pi \: {m}^(3)`

I don't know if these answer are correct, though...