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A candle in the shape of a circular cone has a base of radius r and a height of h that is the same length as the radius. which expresses the ratio of the volume of the candle to its surface area(including the base)? for cone, v=1/3pir^2h and sa=pir^2 pir sqrt r^2 h^2.

User Mike Curry
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2 Answers

6 votes

Rational Expressions QC

1.B

2.C

3.D

4.D

5.B

User Anirudha Mahale
by
7.9k points
2 votes

Answer:


(r(1-√(2)))/(-3)

Explanation:

Volume of cone =
(1)/(3) \pi r^(2) h

Since we are given that a circular cone has a base of radius r and a height of h that is the same length as the radius

=
(1)/(3) \pi r^(2) * r

=
(1)/(3) \pi r^(3)

Surface area of cone including 1 base =
\pi r^(2) +\pi* r * √(r^2+h^2)

Since r = h

So, area =
\pi r^(2) +\pi* r * √(r^2+r^2)

=
\pi r^(2) +\pi* r * √(2r^2)

=
\pi r^(2) +\pi* r^2 * √(2)

Ratio of volume of cone to its surface area including base :


((1)/(3) \pi r^(3))/(\pi r^(2) +\pi* r^2 * √(2))


((1)/(3)r)/(1+√(2))


(r)/(3(1+√(2)))

Rationalizing


(r)/(3(1+√(2))) * (1-√(2))/(1-√(2))


(r(1-√(2)))/(-3)

Hence the ratio the ratio of the volume of the candle to its surface area(including the base) is
(r(1-√(2)))/(-3)

User DanCue
by
8.2k points

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