Step: 1

Volume of a cone = 1 3 πr ^{2}h

[Formula.]

Step: 2

432π = 1 3 x π x r ^{2} x 9

[Substitute the values.]

Step: 3

[Simplify.]

Step: 4

Step: 5

= √ (144 + 9^{2})

[Substitute the values.]

Step: 6

= √ (225) = 15

[Simplify.]

Step: 7

Slant height of the cone = 15 cm.

Correct Answer is : 15 cm

Step: 1

Circumference of the base of a cone = 2πr

[Formula.]

Step: 2

2πr = 132 in.

[Since circumference of a cone is 132 in.]

Step: 3

2 x 22 7 x r = 132

Step: 4

[Simplify.]

Step: 5

Volume of the cone = 1 3 πr ^{2}h

[Formula.]

Step: 6

= 1 3 x 22 7 x 21^{2} x 15

[Substitute the values.]

Step: 7

= 6930

[Simplify.]

Step: 8

Volume of the cone = 6930 in.^{3}.

Correct Answer is : 6930 in.^{3}

Step: 1

Volume of cylindrical part = πr ^{2}h

[Formula.]

Step: 2

= 3.14 x 8^{2} x 15

[Substitute the values.]

Step: 3

= 3014.40

[Simplify.]

Step: 4

Volume of the cylindrical part = 3014.40 m.^{3}.

Step: 5

Volume of Conical part = 1 3 πr ^{2}h

[Formula.]

Step: 6

= 1 3 x 3.14 x 8^{2} x 24

[Substitute the values.]

Step: 7

= 1607.68

[Simplify.]

Step: 8

Volume of the cone = 1607.68 m.^{3}.

Step: 9

Volume of air that occupies the tent = volume of cylindrical part + volume of conical part

= (1607.68 + 3014.40) m.^{3} = 4622.08 m.^{3}

Step: 10

[Round the answer to one decimal place.]

Step: 11

Volume of air that occupies the tent = 4622.1 m.^{3}.

Correct Answer is : 4622.1 m^{3}

Step: 1

Volume of a cone = 1 3 πr ^{2}h

[Formula.]

Step: 2

= 1 3 x πr ^{2} x h

Step: 3

Volume of cone = 1 3 x base area of cone x h

[The base of a cone is a circle.]

Step: 4

154 = 1 3 x 14 x h

[Substitute the values.]

Step: 5

[Multiply each side with 3 14 .]

Step: 6

Height of the cone = 33 in.

Correct Answer is : 33 in.

Step: 1

From the figure, the base diameter of each cone, d = A B = 8 ft

and the height of each cone,h = C O = 18 ft.

and the height of each cone,

Step: 2

The base radius of the cone, r = d i a m e t e r 2

= 8 2

[Substitute diameter = 8 ft.]

Step: 3

= 4 ft

Step: 4

Volume of each cone, V = 1 3 π r ^{2}h

[Formula.]

Step: 5

= 1 3 × π × 4^{2} × 18

[Substitute r = 4 and h = 18.]

Step: 6

= 96π ft^{3}

[Simplify.]

Step: 7

The volume of the figure = 2 × V

[Since the figure contains two identical cones.]

Step: 8

= 2 × 96π ft^{3}

[Substitute, V = 96π ft^{3}.]

Step: 9

= 192π ft^{3}

Step: 10

The volume of the figure is 192π ft^{3}.

Correct Answer is : 192π ft^{3}

Step: 1

Let h be the height of the cone and r be the base radius of the cone.

Step: 2

Volume of the cone, v = (1 3 )π r ^{2}h

[Volume formula.]

Step: 3

The height of the cone, h = 3 v π r 2

Step: 4

= 3 × 7 2 0 π π × 1 2 2

[Substitute v = 720π and r = 12.]

Step: 5

= 15 cm

[Simplify.]

Step: 6

The height of the cone is 15 cm.

Correct Answer is : 15 cm

Step: 1

Let h be the height of the cone and r be the base radius of the cone.

Step: 2

Volume of the cone, v = (1 3 )π r ^{2}h

[Volume formula.]

Step: 3

The height of the cone, h = 3 v π r 2

Step: 4

= 3 × 1 8 0 π π × 6 2

[Substitute v = 180π and r = 6.]

Step: 5

= 15 cm

[Simplify.]

Step: 6

The height of the cone is 15 cm.

Correct Answer is : 15 cm

Step: 1

Volume of a cone, V = 1 3 πr ^{2}h

[Formulae]

Step: 2

[π = 3.141, r = 25, h = 30 and substituting the values]

Step: 3

19631.25 = 19631 cm ^{3}

[Simplify and round the answer to the nearest whole]

Step: 4

Therefore, volume of the cone to the nearest whole unit is 19631 cm^{3}.

Correct Answer is : 19631 cm^{3}

Step: 1

From the figure, the base diameter of each cone, d = AB = 8 cm

and the height of each cone,h = CO = 18 cm.

and the height of each cone,

Step: 2

The base radius of the cone, r = diameter 2

= 8 2

[Substitute diameter = 8 cm.]

Step: 3

= 4 cm

[Divide numerator and denominator by 3.]

Step: 4

Volume of each cone, V = 1 3 π r ^{2}h

[Formula.]

Step: 5

= 1 3 × π × 4^{2} × 18

[Substitute r = 4 and h = 18.]

Step: 6

= 96π cm^{3}

[Simplify.]

Step: 7

The volume of the figure = 2 × V

[Since the figure contains two identical cones.]

Step: 8

= 2 × 96π cm^{3}

[Substitute, V = 96π cm^{3}.]

Step: 9

= 192π cm^{3}

Step: 10

The volume of the figure is 192π cm^{3}.

Correct Answer is : 192π cm^{3}

Step: 1

Let h be the height of the cone and r be the base radius of the cone.

Step: 2

Volume of the cone, v = (1 3 )π r ^{2}h

[Volume formula.]

Step: 3

The height of the cone, h = 3 v π r 2

Step: 4

= 3 × 7 2 0 π π × 1 2 2

[Substitute v = 720π and r = 12.]

Step: 5

= 15 cm

[Simplify.]

Step: 6

The height of the cone is 15 cm.

Correct Answer is : 15 cm

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