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Question 2: The volume of a sphere is 38808 cm3. Find the radius. Use pi = 22/7.
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2 partsStep-by-step solution
11 stepsI can see two questions in the image. I will solve question 2 and question 3.
Part 2· 5 steps
The volume of a sphere
Write down the given formula and values.
The volume of a sphere is given by .
Given volume .
We need to find the radius .
We will use .Substitute the given values into the formula.
Isolate .
Multiply both sides by :
Perform the multiplication and division.
First, divide 38808 by 88:
Now, multiply by 21:
Find the cube root of 9261 to get .
To find the cube root, we can try small integer values or factorize.
We know and .The radius of the sphere is .
Part 3
Solve the expression
Rewrite the expression using fractional exponents.
The expression is .
This can be written as .Simplify the numerator inside the parenthesis.
So the numerator becomes .
Substitute the simplified numerator back into the expression.
Simplify the terms inside the parenthesis by dividing coefficients and subtracting exponents for like bases.
For the coefficients: .
For : .
For : .
For : .So the expression inside the parenthesis simplifies to .
Apply the exponent to each term.
Calculate .
Since and , is not an integer.
We can leave it in this form or approximate it. For exact solution, we leave it as .The simplified expression is .
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