mariasanchez47
Answered

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Would someone please help me?!

1. Which would hold the most water: a bowl in the shape of a hemisphere with a radius r, a cylindrical glass with radius r and height r, or a cone-shaped drinking cup with radius r and height r? Explain.

2. Hari has models of a sphere, a cylinder, and a cone. The sphere's diameter and the cylinder height are the same, 2r. The cylinder has radius r. The cone has diameter 2r and height 2r. Compare the volumes of the cone and the sphere to the volume of the cylinder.

Sagot :

apologiabiology
so
bowl is a half sphere
cylinder is a cylninder
cone is cone

bowl:
area of circle=4/3 pi times r^3
half bowl=4/3 times 1/2 times pi times r^3=2/3pi r^3

cylinder=height times pi times radius^2
this cylinder=r times pi times r^2=pi times r^3


cone=1/3 times height times pi times radius^2
thgis cone=1/3 times r tiimes pi times r^2=1/3 times pi times r^3

compare
bowl=2/3 pi r^3
cylinder=pi r^3
cone=1/3 pi r^3
the cylinder is biggest
CYLINDER IS THE ANSWER




2.
sphwere=4/3 times radius^3 times pi
this sphere=4/3 times pi times r^3

cylinder=height times radius^2 time pi
this cylinder=2r times r^2 times pi=2r^3 times pi

cone=1/3 times height time r^2 times pi
this cone=1/3 times 2r times r^2 times pi=1/3 times 2r^3 times pi=2/3 times r^3 times pi

sphere:4/3 pi r^3
cylinder: 2 pi r^3
cone: 2/3 pi r^3
the height r because it's how tall the water is.
2r is the diameter
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