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Help me with these questions

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help me with these questions 2) Nov 27, 2018

#1
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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
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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

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

24 cm^2   Nov 27, 2018