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help me with these questions

2)

 Nov 27, 2018
 #1
avatar+701 
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The volume of a cylinder: \(\pi r^2 \cdot h\). h = height

 

The radius is 6 cm, and the height is 4*12 = 48 cm. The volume of the cylinder is \(36\pi \cdot 48 = 1728\pi\)

 

The volume of a sphere: \(\dfrac{4}{3} \pi r^3\)

The radius is 6 cm, and \(6^3 \) is 216. \(\dfrac{4}{3} \cdot 216 = 288\). The volume of one sphere is \(288\pi\). If we multiply by 4, the volume of the four spheres is \(1152\pi\)

 

We can calculate the empty cylinder space by subtracting 4 VolumeSphere from VolumeCylinder. We have \(1728\pi - 1152\pi\), which simplifies into \(\boxed{576\pi}\).

 Nov 27, 2018
 #2
avatar+99523 
+1

For the second one we have

 

96 = (1/3) (base area) (height)

 

96 = (1/3)  [ x (3x + 1) ] (12)

 

96 = 4 [x (3x + 1) ]   divide both sides by 4

 

24 = x (3x + 1)  

 

24 = 3x^2 + x      rearrange as

 

3x^2 + x - 24  = 0      factor

 

(3x - 8) ( x + 3) = 0

 

Setting each factor to 0 and solve for x and we have that

 

x = 8/3 cm    or  x = - 3cm

 

Reject the second answer

 

So...the base area is (x) (3x + 1) = (8/3) (3(8/3) + 1 ) = (8/3)(8 + 1) = (8/3)(9) =

 

24 cm^2

 

 

cool cool cool

 Nov 27, 2018

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