Respuesta :

Answer:

1. 170.083 in³

2. 126π in³

3. 92.106 m³

4. 2412.74 in³

5. 612π m³ and 1922 m³

Step-by-step explanation:

1.

Cylinder:

[tex]V = \pi r^{2}h[/tex]               *Plug in numbers*

[tex](3.14)(2.5)^{2}(7)[/tex]         *Square 2.5*

[tex](3.14)(6.25)(7)[/tex]        *Solve*

≈ [tex]137.375in^{3}[/tex]

Sphere:

[tex]V = \frac{4}{3}\pi r^{3}[/tex]              *Plug in numbers*

[tex]\frac{4}{3} (3.14)(2.5)^{3}[/tex]         *Cube 2.5*

[tex]\frac{\frac{4}{3}(3.14)(15.625)}{2}[/tex]         *Divide by 2 and Solve*

≈ [tex]32.7083 in^{3}[/tex]

Add both volumes

[tex]137.375 + 32.7083[/tex] ≈ [tex]170.083in^{3}[/tex]

2.

Cylinder:

[tex]V = \pi r^{2}h[/tex]         *Plug in numbers*

[tex]\pi (3)^{2}(10)[/tex]            *Square 3*

[tex]\pi (9)(10)[/tex]             *Multiply*

[tex]90\pi[/tex]

Sphere:

[tex]V = \frac{4}{3}[/tex] π [tex]r^{3}[/tex]            *Plug in numbers*

[tex]\frac{4}{3}\pi (3)^{3}[/tex]                   *Cube 3*

[tex]\frac{4}{3} \pi (27)[/tex]                   *Multiply*

[tex]36\pi[/tex]

Add both Volumes to get total

[tex]90\pi + 36\pi = 126in^{3}[/tex]

3.

Sphere:

[tex]V = \frac{4}{3}\pi r^{3}[/tex]              *Plug in numbers*

[tex]\frac{4}{3} (3.14)(3)^{3}[/tex]            *Cube 3*

[tex]\frac{4}{3} (3.14)(27)[/tex]            *Multiply*

[tex]113.04m^{3}[/tex]

Cone:

[tex]V = \frac{\pi r^{2}h}{3}[/tex]             *Plug in numbers*

[tex]\frac{(3.14)(2)^{2}(5)}{3}[/tex]           *Square 2*

[tex]\frac{(3.14)(4)(5)}{3}[/tex]             *Solve*

[tex]20.93m^{3}[/tex]

Subtract the volumes to get the volume of the blue area

[tex]113.04 - 20.93 = 92.106m^{3}[/tex]

4.

Sphere:

[tex]V = \frac{4}{3} \pi r^{3}[/tex]            *Plug in numbers*

[tex]\frac{4}{3}\pi (8)^{3}[/tex]                 *Cube 8*

[tex]\\\frac{4}{3}\pi (512)[/tex]               *Multiply*

[tex]\\\\\pi (682.6)[/tex]              *Solve*

[tex]2133.66in^{3}[/tex]           *Divide by 2 since it's a hemisphere*

Cone:

[tex]V = \frac{\pi r^{2}h}{3}[/tex]            *Plug in numbers*

[tex]\frac{\pi (8)^{2}(20)}{3}[/tex]              *Square 8*

[tex]\frac{\pi (64)(20)}{3}[/tex]              *Multiply and Divide*

[tex]1340.41 in^{3}[/tex]

Add both volumes

[tex]1072.33 + 1340.41 = 2412.74in^{3}[/tex]

5.

Cylinder:

[tex]V = \pi r^{2}h[/tex]            *Plug in numbers*

[tex]\pi (6)^{2}(16)[/tex]              *Square 6*

[tex]\pi (36)(16)[/tex]             *Multiply*

[tex]576\pi[/tex]

Cone:

[tex]V = \frac{\pi r^{2}h}{3}[/tex]            *Plug in numbers*

[tex]\frac{\pi (6)^{2}3}{3}[/tex]                  *Square 6*

[tex]36\pi[/tex]

Add both volumes

[tex]576\pi + 36\pi = 612\pi m^{3}[/tex]

Alternative: *Multiply π*

[tex]1922m^{3}[/tex]

amuratov

Answer:

1) 175 [tex]in^2[/tex]

2) 1st option

3) 92 [tex]m^2[/tex]

4) 2412 [tex]in^3\\[/tex]

5) 2nd option

Step-by-step explanation:

[tex]1)\ A = D * Pi = 5 * 3.14 = 15.7\\[/tex]

[tex]2)\ V_{1} = 15.7 * 7 = 109.9[/tex]

[tex]3)\ V_{2} = 4Pi*\frac{R^3}{3} = 12.56*\frac{15.625}{3} = 65.41(6)[/tex]

[tex]4)\ V_1 + V_2 = 65.4 + 109.9 = 175.3[/tex] which is close to 175

[tex]1)\ A = Pi * R^2 = 3.14 * (\frac{6}{2})^2 = 3.14 * 3^2 = 28.26\\[/tex]

[tex]2)\ V_1 = A * h = 28.26 * 10 = 282.6[/tex]

[tex]3)\ V_2 = \frac{4}{3} * Pi * R^3 = \frac{4}{3} * 3.14 * (\frac{6}{2})^3 = 113.04[/tex]

[tex]4)\ V_1 + V_2 = 282.6 + 113 = 395.6[/tex] which is very close to 396

[tex]5)\ 396 = 126 * pi[/tex]

[tex]1) V_1 = \frac{1}{3} * Pi * R^2 * h = \frac{1}{3} * 3.14 * 2^2 * 5 = 20.9(3)[/tex] =

[tex]2)\ V_2 = \frac{4}{3} * Pi * R^3 = \frac{4}{3} * 3.14 * 3^3 = 113.04\\[/tex]

[tex]3)\ V_2 - V_1 = 113.04 - 20.93 = 92.14[/tex] which is very close to 92

[tex]1)\ V_1 = \frac{\frac{4}{3} * Pi * R^3}{2} = \frac{\frac{4}{3} * 3.14 * 512}{2} = 1,071.786\\[/tex]

[tex]2)\ V_2 = \frac{1}{3} * Pi * R^2 * h = \frac{1}{3} * 3.14 * 64 * 20 = 1,339.733[/tex]

[tex]3)\ V_1 + V_2 = 1072 + 1340 = 2,411 = 2412[/tex]

[tex]1)\ A = Pi * R^2 = 36*Pi\\[/tex]

[tex]2)\ V_1 = 36*Pi * 16 = 576 * Pi\\[/tex]

[tex]3)\ V_2 = \frac{1}{3} * Pi * R^2 * h = \frac{1}{3} * Pi * 36 * 3 = 36 * Pi[/tex]

[tex]4) V_1 + V_2 = 576Pi + 36Pi = 612Pi[/tex]

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