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lgloos. During long journeys, some Canadian Eskimos built winter houses of snow blocks stacked in the dome shape shown. Estimate the volume of an igloo having an interior height of 5.5 feet to the nearest cubic foot.
$$348 \mathrm{ft}^{3}$$
Precalculus
Algebra
Chapter 2
Equations, Inequalities, and Problem Solving
Section 4
Formulas
Algebra Topics That are Reviewed at the Start of the Semester
Equations and Inequalities
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this problem. We're being asked to find the volume of this igloo, while they tell us is in the shape of a dome. Well, that means it's half of what a feat a sphere would be because the sphere would be the other half of this shape. Well, how do we find the volume of a sphere? Well, it's the formula. V equals 4/3 pi are cute, but also noticing Kate, in this case that were only trying to find half of it. So what we can do to find the volume of this igloo is we can then multiply this formula by 1/2 so we'll have V equals 1/2 times, 4/3 pi are cute. Well, 1/2 times 4/3 is equal to 2/3. So we'll have V equals 2/3 pi are cute. And if you know this, even though the height is 5.5 feet, that really represents the radius in this case. So what we're gonna do is we're gonna substitute 5.5, and for our we're gonna have V equals 2/3 times pi times 5.5 to the third. And now we simply need to evaluate this. Well, first thing we need to do is 5.5. Race to the third power. And because I'm running out of room, I'm gonna come back to the top. So we're gonna have V equals 2/3 pi times will 5.5 to the third is 1 66.375 Next, we need to multiply 1 66.375 by 2/3. And when we do that, we will have V equals 1 10 0.9166667 pi. Now we see Simply need to multiply this by pi. Now, if you don't have a pie button on your calculator, you can use 3.14 Otherwise, you should use the pikey, which is what I have. So we're left with 3 48 0.454 9852 No, we're being asked for in our final answer to the round to the nearest cubic foot. Never words to nearest hole number. Well, that means we need to look at that number after the decimal place, which is a four to determine whether this H around upper state the same Well, because the number after the Dust Bowl is a four and it's less than five. We're going to keep the eight and eight. So what we find is that our volume will be 340 and remember, the units for volume are cubic feet, so we'll have feet cute.
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