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Volume of Cone

Concept Explanation

Volume of Cone

Cone: A cone is a three-dimensional figure with one circular base. A curved surface connects the base and the vertex.

Volume of Cone: .The volume V of a cone with radius r is one-third the area of the base B times the height h.

Volume of the cone of radius r and height h = $frac{1}{3}{pi}r^{2}h$

Illustration: Find the volume of a right circular cone 1.02m high , if the radius of its base is 28 cm.

Solution: We know that the volume V of a right circular cone of radius r and height h is given $V=frac{1}{3}{pi}r^{2}h$ . Here, r = 28cm and h = 1.02 m = 1.02 X 100 cm = 102 cm

$therefore V=frac{1}{3}times {frac{22}{7}}times 28times 28times 102=83776;cm^3$

Illustration: A conical tent is 9 m high and the radius of its base is 12 m.

(i) What is the cost of the canvas required to make it, if a square metre canvas costs Rs 10?

(ii) How many persons can be accommodated in the tent, if each person requires 2 square metre on the ground and $15;m^{3}$ of space to breath in?

Solution: We have,

r = Radius of the base of the conical tent = 12 m

h = Height of the conical tent = 9 m

l = Slant height of the conical tent = $sqrt{r^{2}+h^{2}}$

$=sqrt{(12)^{2}+9^{2}}$

$=sqrt{144+81}$ $=sqrt{225};m$

$=15;m$

(i) Area of the lateral surface = $pi rl=frac{22}{7}times 12times 15;m^{2}$

$=565.7;m^{2}$

So, total cost of the canvas = Rs(565.2 X 10) = Rs 5652

(ii) Area of the base of the conical tent = $pi r^{2}=frac{22}{7}times 12times 12;m^{2}$

$=452.16;m^{2}$

As each person requires 2 sq. metres of floor area.

So, max number of persons who will have enough space on the ground $=frac{452.16}{2}=226$

Also, Volume of the conical tent $=frac{1}{3}times Area;of;the;basetimes Height$

Volume of the conical tent $=frac{1}{3}times 452.16times 9;m^{3}$

Volume of the conical tent = 1356.48 $;m^{3}$

We have, air space required person $=15;m^{3}$

So, number of persons who will have enough air space to breath in $=frac{1356.48}{15}=90$

Between 226 and 90, the smaller number is 90.

Hence 90 persons can be accomodated.

Sample Questions

(More Questions for each concept available in Login)

Question : 1

The area of the base of a right circular cone is $314;cm^{2}$ and its height is 15 cm. Find the volume of the cone.
A. $1507;cm^{3}$	B. $5570;cm^{3}$	C. $1570;cm^{3}$	D. $1577;cm^{3}$
Right Option : C
View Explanation

Question : 2

The base radii of two right circular cones of the same height are in the ratio 3:5. Find the ratio of their volumes.
A. 25:9	B. 9:25	C. 9:16	D. 16:9
Right Option : B
View Explanation

Question : 3

A right circular cone is 3.6 m high and radius of its base is 1.6 cm. It is melted and recast into a right circular cone with radius of its base as 1.2 cm. Find its height.
A. 6.4 cm	B. 5.3 cm	C. 7.3 cm	D. 5.6 cm
Right Option : A
View Explanation

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