(Volume = πr

Step: 1

The volume of a cylinder = π r ^{2}h

[Formula.]

Step: 2

= π × 7^{2} × 9

[Substitute r = 7 and h = 9.]

Step: 3

= 441π in ^{3}

[Simplify.]

Step: 4

So, the volume of the cylinder that Johnny made is 441π in ^{3}.

Correct Answer is : 441π in^{3}

Step: 1

Length of the water tank = 60 ft.

Step: 2

Width of the water tank = 40 ft.

Step: 3

The height of the water level = 20 ft.

Step: 4

Volume of water in the tank = length × width × depth.

Step: 5

= 60 × 40 × 20

[Substitute l = 60, w = 40 and h = 20.]

Step: 6

= 48000 ft^{3}

[Multiply 60, 40 and 20.]

Step: 7

Volume of water in the tank is 48000 ft^{3}.

Correct Answer is : 48000 ft^{3}

Step: 1

Volume of a cylinder = Base area × height of the cylinder

Step: 2

= 7 × 5

[Substitute the values.]

Step: 3

= 35 in.^{3}

[Multiply.]

Step: 4

So, the volume of the cylinder is 35 in.^{3}.

Correct Answer is : 35 in.^{3}

Step: 1

The formula for the volume of a cylinder is π r ^{2}h , where r is the radius of its base and h is its height.

Step: 2

Volume of the cylinder = π × 3^{2} × 21

[Substitute the values of the base radius and the height.]

Step: 3

= 22 7 × 9 × 21

[Substitute π = 22 7 .]

Step: 4

= 4158 7

[Multiply the numbers in the numerator.]

Step: 5

= 594

[Divide.]

Step: 6

So, the volume of the cylinder is 594 cubic units.

Correct Answer is : 594 cubic units

Step: 1

Base diameter of cylindrical tank =24 cm

Step: 2

Radius = diameter 2 = 24 2 = 12 cm.

Step: 3

Capacity of a cylindrical tank = π r ^{2}h

[Formula.]

Step: 4

Step: 5

3.14 × 12^{2} × h = 7687

[Substitute the values.]

Step: 6

452.16 h = 7687

[Multiply.]

Step: 7

[Divide each side by 452.16]

Step: 8

[Simplify.]

Step: 9

[Round to the nearest cm.]

Step: 10

Height of the cylindrical tank = 17 cm

Correct Answer is : 17 cm

Step: 1

Let r and h be the radius and height of the cylinder, respectively.

Step: 2

Volume of the cylinder = π r ^{2}h

[Formula.]

Step: 3

The height of the cylinder, after increasing it by 8 times is 8h .

Step: 4

Volume of the cylinder after increasing its height = π × r ^{2} × 8h

[Substitute h = 8h .]

Step: 5

= 8π r ^{2}h

[Simplify.]

Step: 6

= 8 × original volume of the cylinder

Step: 7

So, the volume of the cylinder becomes 8 times the original volume.

Correct Answer is : 8 times

Step: 1

Inner radius of the tank = d 2 = 2 m = 200 cm

[Radius = Diameter 2 .]

Step: 2

Outer radius of the tank = 200 + 30 = 230 cm

[Radius + thickness of the tank.]

Step: 3

Height of the tank = 80 cm

[Given.]

Step: 4

Volume of the tank = Volume of outer cylinder - Volume of the inner cylinder

[Formula.]

Step: 5

Volume of the outer cylinder = 3 × (230)^{2} × 80 = 12696000 cm^{3}

[Volume of the cylinder = π r ^{2} h .]

Step: 6

Volume of the inner cylinder = 3 × (200)^{2} × 80 = 9600000 cm^{3}

[Volume of the cylinder = π r ^{2} h .]

Step: 7

Volume of the tank = 12696000 - 9600000 = 3096000 cm^{3} = 3.096 m^{3}

[Substitute in step 4.]

Step: 8

Rate of construction = $10 per m^{3}

[Given.]

Step: 9

Cost of construction = 3.096 m^{3} × 10 = $30.96

[Simplify.]

Correct Answer is : $30.96

Step: 1

Number of chains that can be made = Volume of the golden bar Volume of one chain

[Formula.]

Step: 2

Volume of the golden bar = 1.20 × 100 ×16 × 15 = 28800 cm^{3}

[Convert meter to centimeter.]

Step: 3

Radius of the chain = 5 2 = 2.5 mm = 0.25 cm

[Radius = Diameter 2 .]

Step: 4

Volume of one chain = 3 × (0.25)^{2} × 56 = 10.50 cm^{3}

[Volume of a cylinder = π r ² h .]

Step: 5

Number of chains = 28800 10.50 = 2743 chains (approximately)

[From steps 2 and 4.]

Correct Answer is : 2743

Step: 1

Let r and h be the radius and height of the cylinder, respectively.

Step: 2

Volume of the cylinder = π r ^{2}h

[Formula.]

Step: 3

The height of the cylinder, after increasing it by 3 times is 3h .

Step: 4

Volume of the cylinder after increasing its height = π × r ^{2} × 3h

[Substitute h = 3h .]

Step: 5

= 3π r ^{2}h

[Simplify.]

Step: 6

= 3 × original volume of the cylinder

Step: 7

So, the volume of the cylinder becomes 3 times the original volume.

Correct Answer is : 3 times

Step: 1

Volume of a cylinder = base area × height of the cylinder

Step: 2

= 8 in.^{2} × 5 in.

[Substitute the values.]

Step: 3

= 40 in.^{3}

[Multiply.]

Step: 4

So, the volume of the cylinder is 40 in.^{3}.

Correct Answer is : 40 in.^{3}

Step: 1

The formula for the volume of a cylinder is π r ^{2}h , where r is the radius of its base and h is its height.

Step: 2

Volume of the cylinder = π × 4^{2} × 14

[Substitute the values of the base radius and the height.]

Step: 3

= 22 7 × 16 × 14

[Substitute π = 22 7 .]

Step: 4

= 4928 7

[Multiply the numbers in the numerator.]

Step: 5

= 704

[Divide.]

Step: 6

So, the volume of the cylinder is 704 cubic units.

Correct Answer is : 704 cubic units

Step: 1

The volume of a cylinder = π r ^{2}h

[Formula.]

Step: 2

= π × 2^{2} × 8

[Substitute r = 2 and h = 8.]

Step: 3

= 32π cm ^{3}

[Simplify.]

Step: 4

So, the volume of the cylinder that Johnny made is 32π cm ^{3}.

Correct Answer is : 32π cm^{3}

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