Read the following , understand the mathematical idea expressed in it and answer the question ?
1)The volume of a cone is the one-third of the product of it's Base area and Height .The curved surface area of a cone is half the product of base circumstances and height ?
2)A cylinder of wax has radius 6cm and height 8cm a cone of largest size is curved from it ?
sub question
a) What is the radius ?
b) What is the slant height of the cone?
c) Find the volume of the cone?
d) What is the CSA ?
e) The remained wax is used to make candle with 1cm radius and 8cm height ?
sub question of e question
a) Find the volume of the candle?
b) How many can we make ?
Answers
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Step-by-step explanation:
1.Consider the given slant height l and radius=r of the cone,
Curved surface area=(Arc length of sector/Circumference of circle)×Area of circle Curved surface area
=
2πl
2πr
×πl
2
=πrl
2.Volume of the sphere=
3
4
π.5
3
=
3
500
π
Volume of the cone =
3
1
πr
2
.
2
5
=
6
5
πr
2
∴
6
5
πr
2
=
3
500
π⇒r=10
3.(a) Volume of cone =
3
1
πr
2
h=
3
1
π(6)
2
12=144πcm
3
(b) Volume of cylinder =πr
2
h=π(6)
2
12=432πcm
3
Volume of remaining wax =432π−144π=288πcm
3
Volume of one candle =πr
2
h=π×1
2
×12=12πcm
3
Thus, number of candles =
12π
288π
=24
Thus, number of candles is 24.
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