MATH SOLVE

3 months ago

Q:
# The volume of a cone is 88π cubic feet. Its height is 8 feet. Fatima is finding the radius of the cone. Her work is shown below. Step 1: 88π = 1/3 πr² (8)Step 2: 88π = 8/3 πr² Step 3: 8/3 (88) = r² Step 4: 234.7 = r² Step 5: 15.3 =r What is Fatima's error? - In step 4, Fatima did not find the correct value of 8/3 (88).- In step 2, Fatima should not have multiplied 1/3 and 8. - In step 3, Fatima did not multiply 88 by the reciprocal of 8/3 - In step 1, Fatima did not substitute the correct value for the height in the formula.

Accepted Solution

A:

To evaluate the radius of the cone we proceed as follows:

V=1/3 πr²h

plugging in the values, v=88π, h=8 ft

step 1

88π1/3πr²(8)

step 2

88π=8/3πr²

step 3

divide both sides by π

88=8/3r²

multiply both sides by 3/(8)

88(3/8)=r²

step 4

simplify

33=r²

step 5

get the square root

r=√33

Thus the mistake that Fatima made was:

In step 3, Fatima did not multiply 88 by the reciprocal of 8/3

V=1/3 πr²h

plugging in the values, v=88π, h=8 ft

step 1

88π1/3πr²(8)

step 2

88π=8/3πr²

step 3

divide both sides by π

88=8/3r²

multiply both sides by 3/(8)

88(3/8)=r²

step 4

simplify

33=r²

step 5

get the square root

r=√33

Thus the mistake that Fatima made was:

In step 3, Fatima did not multiply 88 by the reciprocal of 8/3