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 × 4 8 0 π π × 1 2 2

[Substitute v = 480π and r = 12.]

Step: 5

= 10 cm

[Simplify.]

Step: 6

The height of the cone is 10 cm.

Correct Answer is : 10 cm

Step: 1

Let r be the radius of the cone.

Step: 2

Volume of the cone, V = (1 3 )πr ^{2}h

[Formula.]

Step: 3

[Rewrite the formula.]

Step: 4

= 3 × 4 8 π π × 4

[Substitute V = 48π and h = 4.]

Step: 5

= 6 ft

[Simplify.]

Step: 6

The base radius of the cone is 6 ft.

Correct Answer is : 6 ft

Step: 1

From the figure, the base radius of each cone, r = 7.5 cm

and the height of each cone,h = 12.5 cm

and the height of each cone,

Step: 2

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

[Volume formula.]

Step: 3

= 1 3 × π × (7.5)^{2} × 12.5

[Substitute r = 7.5 and h = 12.5.]

Step: 4

= 234.37π cm^{3}

[Simplify.]

Step: 5

The volume of the figure = 2 × V

[The figure contains two identical cones.]

Step: 6

= 2 × 234.37π

[Substitute V = 234.37π .]

Step: 7

= 468.74π cm^{3}

Step: 8

The volume of the figure is 468.74π cm^{3}.

Correct Answer is : 468.74π cm^{3}

Step: 1

Step: 2

Volume of the cone = 1 3 πr ^{2}h

[Formula.]

Step: 3

= 1 3 × π × 4.6^{2} × 6.9

[Substitute base radius, r = 4.6 cm and height, h = 6.9 cm.]

Step: 4

= 1 4 6 π 3

[Divide numerator and denominator by 3.]

Step: 5

= 48.67π

[Simplify.]

Step: 6

The volume of the cone is 48.67π cm^{3}.

Correct Answer is : 48.67π cm^{3}

Step: 1

The base radius of the cone, r = d i a m e t e r 2 = 13.8 2 = 6.9 cm

[Since, the diameter of the cone is 13.8 cm.]

Step: 2

From the figure, A B ^{2} + B C ^{2} = A C ^{2}

[Pythagorean theorem.]

Step: 3

[Substitute A B = h , B C = 6.9 cm, and A C = 11.5 cm.]

Step: 4

47.6 + h ^{2} = 132.3

[Evaluate powers.]

Step: 5

[Subtract 47.6 from both sides.]

Step: 6

Step: 7

[Take square root on both sides.]

Step: 8

The height of the cone is 9.2 cm.

Step: 9

The volume of the cone = 1 3 πr ^{2}h

[Volume formula.]

Step: 10

= 1 3 × π × (6.9)^{2} × 9.2

[Substitute r = 6.9 and h = 9.2.]

Step: 11

= 146π cm^{3}

[Simplify the expression.]

Step: 12

The volume of the cone is 146π cm^{3}.

Correct Answer is : 146π cm^{3}

Step: 1

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

= 18 2 = 9 ft

[Since the diameter of the cone is 18 ft.]

Step: 2

From the figure, AB^{2} + BC^{2} = AC^{2}

[Pythagorean theorem.]

Step: 3

[Substitute AB = h , BC = 9 ft, and AC = 15 ft.]

Step: 4

[Evaluate powers.]

Step: 5

[Subtract 81 from both sides.]

Step: 6

[Subtract.]

Step: 7

[Take square root on both sides.]

Step: 8

The height of the cone is 12 ft.

Step: 9

The volume of the cone = 1 3 πr ^{2}h

[Volume formula.]

Step: 10

= 1 3 × π × 9^{2} × 12

[Substitute r = 9 and h = 12.]

Step: 11

= 324π ft^{3}

[Simplify the expression.]

Step: 12

The volume of the cone is 324π ft^{3}.

Correct Answer is : 324π ft^{3}

Step: 1

Height of a cone = base radius of the cone = 3r mm.

Step: 2

Volume of a cone = 1 3 π r ^{2}h

[Formula.]

Step: 3

= 1 3 × π × (3r )^{2} × 3r

[Substitute the values.]

Step: 4

= 9π r ^{3}

[Simplify.]

Step: 5

The volume of the right circular cone = 9πr ^{3} mm^{3}.

Correct Answer is : 9πr ^{3} mm^{3}

Step: 1

Base radius of the new cone = 2 × radius of the initial cone = 2 × 4 = 8 in.

[Since base radius of new cone is double the radius of initial cone.]

Step: 2

Height of the new cone = 2 × height of the initial cone = 2 × 7.5 = 15 in.

[Since height of new cone is double the height of initial cone.]

Step: 3

Volume of cone = 1 3 πr ^{2}h

[Formula.]

Step: 4

Volume of new cone = 1 3 × π × 8^{2} × 15

= 1004.8

[Substitute the values in the formula and simplify.]

Step: 5

Volume of the new cone is 1004.8 in.^{3}.

Correct Answer is : 1004.8 in.^{3}

Step: 1

Curved surface area of cone = πrl

[Formula.]

Step: 2

πrl = 423.9

[Since curved surface area of cone is 423.9 cm^{2}.]

Step: 3

3.14 × 9 × l = 423.9

[Substitute the values of π and r .]

Step: 4

[Simplify.]

Step: 5

Slant height of the cone (l ) = 15.

Step: 6

Height of cone^{2} = slant height of cone^{2} - radius^{2}.

Step: 7

Height of cone^{2} = 15^{2} - 9^{2}

[Substitute the values.]

Step: 8

Height of the cone = 12 cm

[Take the square root of each side.]

Step: 9

Volume of cone = 1 3 π r ^{2}h

[Formula.]

Step: 10

= 1 3 × 3.14 × 9^{2} × 12

[Substitute the values.]

Step: 11

= 1017.36

[Simplify.]

Step: 12

[Round the answer to the nearest whole number.]

Step: 13

Volume of the cone = 1017 cm^{3}.

Correct Answer is : 1017 cm^{3}

Step: 1

Volume of a cone = 1 3 πr ^{2}h

[Formula.]

Step: 2

1024π = 1 3 × π × r ^{2} × 12

[Substitute the values.]

Step: 3

[Simplify.]

Step: 4

Slant height of cone (l ) = r 2 + h 2

Step: 5

= ( 2 5 6 + 1 2 2 )

[Substitute the values.]

Step: 6

= 4 0 0 = 20

[Simplify.]

Step: 7

Slant height of the cone = 20 cm.

Correct Answer is : 20 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 × 22 7 × r = 132

Step: 4

[Simplify.]

Step: 5

Volume of the cone = 1 3 πr ^{2}h

[Formula.]

Step: 6

= 1 3 × 22 7 × 21^{2} × 21

[Substitute the values.]

Step: 7

= 9702

[Simplify.]

Step: 8

Volume of the cone = 9702 in.^{3}

Correct Answer is : 9702 in.^{3}

Step: 1

Volume of cylindrical part = πr ^{2}h

[Formula.]

Step: 2

= 3.14 × 8^{2} × 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 × 3.14 × 8^{2} × 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 the cup, V = 1 3 π R^{2} H

[Volume of the cone = 1 3 π r^{2} h.]

Step: 2

Volume of the part of the conical cup containing liquid in it, v = 1 3 π r ^{2}h

Step: 3

Consider ΔABC and ΔDEC, R r = H h

[As ΔABC and ΔDEC are similar triangles.]

Step: 4

[Given, h = H 2 .]

Step: 5

[Simplify.]

Step: 6

Step: 7

[Formula.]

Step: 8

[Volume of the liquid = 3 ounces.]

Step: 9

[From steps 4 and 5.]

Step: 10

V = 3 × 4 × 2

[Multiply with 3 on both sides.]

Step: 11

V = 24 ounces

[Simplify.]

Step: 12

So, the volume of the liquid required to fill the entire conical cup = 24 ounces

Correct Answer is : 24 ounces

Step: 1

Base radius of the new cone = 2 × radius of the initial cone = 2 × 6 = 12 in.

[Since base radius of new cone is double the radius of initial cone.]

Step: 2

Height of the new cone = 2 × height of the initial cone = 2 × 22.50 = 45 in.

[Since height of new cone is double the height of initial cone.]

Step: 3

Volume of cone = 1 3 πr ^{2}h

[Formula.]

Step: 4

Volume of new cone = 1 3 × 3 × 12^{2} × 45

= 6480

[Substitute the values in the formula and simplify.]

Step: 5

Volume of the new cone is 6480 in.^{3}.

Correct Answer is : 6480 in.^{3}

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