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Numerade Educator



Problem 68 Hard Difficulty

A bowl is shaped like a hemisphere with diameter 30 cm. A heavy ball with diameter 10 cm is placed in the bowl and water is poured into the bowl to a depth of $ h $ centimeters. Find the volume of water in the bowl.




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Video Transcript

The problem is a ball is shipped to like, Ah, hemisphere with damages thirty centimeters Highway war was down. May to ten centimetres is placed in the ball on the water is poured into the war to adapts of h centimeters kind of the volume of water in the ball. But this problem we have two cases. One is which is smaller, isn't it? Can on another is which is greater than ten on DH smalls and fifteen the less compute the first two case. In this case for any cross section. It is our washer. So you find you know it. It's a distance. He trains this cross section on Dax is the court. Why send in a riders this part? It's the culture. Ah, squire minus have to r minus R minus y squared. Oh, here. Smart too. Love, Capt R is because too fifteen. This is a country return. This one statistics he could chew. You're tough. Twelve square, minus ten. Minus y square on DH out of riders. Is he called Tio No. Fifteen square, minus y squared. Then we're half body. Um, we caught you into grow from fifteen minus age. Teo fifteen. Hi squired off this square. So this's fifteen squire, minus life square minus and five minus. And mine's why, squire? Yeah. Why? This is culture into girl from fifteen. Minus age two fifteen. Hi, This is fifteen squire minus lie square, minus fifteen minus times Pfaff Glass one hundred minus twenty. Why past y squared? You know why this is a culture into girl fifteen miles age. You're fifteen high times three hundred minus twenty y you want? So this is the culture. Hi. Three hundred. And why? Minus ten? Wise squire from fifteen miles age two. Fifteen. So this it's cultural pie. Homs three hundred Nate minus ten times fifteen squire, minus fifteen square miles. They're the age class A square. So the answer is this is equally true. Hi Times Square. Second case h is greed is on turn a small fifteen. In this case, the first just graph the first on which is equal to ten with half from the first case we have. If you got to ten with half. This is the cultural pie temp I hams It squares that this is equal to one thousand. Hi. Tens of volume three is the culture one thousand glass into girl from fifteen miles Age to above Hi times fifteen Schooling minus y squared You know why Things The cross section is a disc on its various Izzy culture. Lucia fifteen square minus y square. So this's equal to myself and the pie class. High times fifteen squire. Why minus one third Last cube from fifteen minus Stage two Bob, That just is cultural. My Starland Pie plus high times fifteen squire um H minus ten minus one third Time's off. Cuba minus fifteen minus stage Cube. This is Hunter for H is greater than ten on smaller than fifteen.