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Celeste made 6 cone shaped ice blocks that each have a radius of 2.8 in. and a height of 7 in. She used a cylindrical container with a radius of 9 in. to fill all of the cones. What is the height of the cylindrical container? Use 3.14 to approximate pi and round your answer to two decimals places. show your work.

Relax

Respuesta :

Volume (cone) = (1/3)(b x  h)
b=base
h=height
1) we calculate the total volume of the 6 cones:
Total volume of the 6 cones.=6(1/3)(b x h=2(b x h)
base: πr²=π(2.8 in)²=7.84 in²

Total volume=2(7.84π in² * 7 in)=109.76π in³

2) we calculate the Volume of the cylindrical container.
Volume (cylinder)=base * height
base=πr²=π(9 in)²=81π in²

Volume=(81π in² * h)=81πh in²

Therefore:
Volume  of the 6 cones= volume of the cylinder
109.76π in³=81πh in²
h=(109.76π in³) / (81π in²)=1.3550 in≈1.36 in

Answer: The height is 1.36 in.

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