Question

I just need to know the answers to the picture

Answer 1

6.

`48\pi \: {ft}^(3)`

7.

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

8.

`112 \: {in}^(3)`

9.

`14.52\pi \: {cm}^(3)`

10.

`68.75\pi \: {yd}^(3)`

11.

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

12. h ≈ 3,3 yd

13. h ≈ 5,5 m

14. V ≈ 77,0 in^3

15. V ≈ 69,1 in^3

16. V ≈ 8517,0 in^3

17. V ≈ 2628,1 cm^3

Explanation:

6.

`v = \pi {r}^(2) * h`

`v = \pi * {4}^(2) * 3 = 48\pi`

.

7.

`v = {9}^(2) * \pi * 1 = 81\pi`

.

8.

`v = {4}^(2) * \pi * 7 = 112\pi`

.

9.

`v = ( {2.2})^(2) * \pi * 3 =14.52\pi`

.

10. r = 0,5 × d

r = 0,5 × 5 = 2,5 yd

`v = ({2.5})^(2) * \pi * 11 = 68.75\pi`

.

11. r = 0,5 × 4,6 = 2,3 m

`v = ({2.3})^(2) * \pi * 6.1 = 32.269\pi`

.

12. V = 41,5 yd^3

r = 2 yd

`v = \pi * {r}^(2) * h`

`41.5= \pi * {2}^(2) * h`

`h = (41.5)/(4\pi) = (83)/(8\pi) ≈3.3`

.

13. d = 1,5 m

r = 0,5 × 1,5 = 0,75 m

V = 9,7 m^3

`v = \pi {r}^(2) * h`

`9.7 = \pi * ( {0.75})^(2) * h`

`h = (9.7)/(0.5625\pi) ≈5.5`

.

14. Given:

h = 8 in

d = 3,5 in

Find: V - ?

First, let's find the radius:

r = 0,5 × 3,5 = 1,75

`v = \pi {r}^(2) * h`

`v = \pi *( {1.75})^(2) * 8 =24.5\pi≈77.0`

.

15 Given:

h = 5,5 in

d = 4 in

Find: V - ?

First, let's find the radius:

r = 0,5 × 4 = 2 in

`v = \pi {r}^(2) * h`

`v = \pi * {2}^(2) * 5.5 = 22\pi≈69.1`

.

16. This figure contains 2 cilinders and one rectangular prism

First, let's find the volume of 2 cilinders (r = 0,5 × 25 = 12,5 in)

`v(both \: cilinders) = (\pi * ({12.5})^(2) * 4 ) * 2= 1250\pi`

`v(prism) = 30 * 17 * 9 = 4590`

`v(total) = 1250\pi + 4590≈8517.0`

.

17. This figure contains one rectangular prism and two semi-cilinders

First, let's find the volume of 2 semi-cilinders (it counts as one cilinder, since there's 2 identical halves, also r = 0,5 × 8 = 4):

`v(cilinder) = \pi * {4}^(2) * 23 = 368\pi`

`v(prism) = 23 * 8 * 8 = 1472`

`v(total) = 368\pi + 1472≈2628.1`