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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.

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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