Question

I REALLY NEED HELP!
A sphere of metal with diameter 8cm is melted down.
It is then formed in to a trapezoidal prism as shown below.
The cross-sectional area (A) is 10cm2. What is the depth of trapezium?Volume of a sphere=4/3 πr³
Surface area of a sphere = 4πr²


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Answer 1

Fun.  

The volume of the prism is just going to be the base area A times the depth x.

That's equal to the volume of the sphere.

$Ax = \dfrac{4}{3} \pi r^3$

$x = \dfrac{4 \pi r^3}{3A}$

We have r=8/2=4, A=10.

$x = \dfrac{4 \pi (4)^3}{3(10)} = \dfrac{128 \pi}{15} \approx 28.808$

The exact answer is

Answer: 128π/15  cm