Yohan is blowing up a spherical balloon. He blows 108π cubic centimeters of air with every breath. It takes him 72 breaths to fully inflate the balloon. What is the radius of the balloon in centimeters when it is fully inflated?
Q. Yohan is blowing up a spherical balloon. He blows 108π cubic centimeters of air with every breath. It takes him 72 breaths to fully inflate the balloon. What is the radius of the balloon in centimeters when it is fully inflated?
Calculate Total Volume: Calculate the total volume of air Yohan blew into the balloon.Since Yohan blows 108π cubic centimeters of air with every breath and it takes him 72 breaths to inflate the balloon, we can calculate the total volume by multiplying the volume per breath by the number of breaths.Total volume = Volume per breath * Number of breathsTotal volume = 108πcm3/breath×72breathsTotal volume = 7776πcm3
Use Sphere Volume Formula: Use the formula for the volume of a sphere to find the radius.The volume V of a sphere is given by the formula V=34πr3, where r is the radius of the sphere.We can set the total volume equal to this formula and solve for r.7776πcm3=34πr3
Isolate r3: Isolate r3 on one side of the equation.To do this, we divide both sides of the equation by (4/3)π.(7776π cm3)/((4/3)π)=r3r3=(7776π cm3)/((4/3)π)r3=(7776/4)×3 cm3r3=1944×3 cm3r3=5832 cm3
Take Cube Root: Take the cube root of both sides to solve for r.r=35832 cm3r≈18 cm
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