Step: 1

The volume of the sphere = 256 cm^{3}

Step: 2

Let r be the radius of the sphere.

Step: 3

The volume of the sphere V = 4 3 πr ^{3}

Step: 4

Step: 5

[Substitute π = 3.]

Step: 6

Step: 7

= 64

[Divide 256 by 4.]

Step: 8

Step: 9

= 4 cm

[Simplify.]

Step: 10

The base radius of the sphere is 4 cm.

Correct Answer is : 4 cm

Step: 1

The side of the cube is 24 cm.

[Given.]

Step: 2

The maximum radius of sphere that can be carved out of the cube = 24 2 = 12 cm.

Step: 3

The maximum volume of the sphere that can be carved out of the cube = 4 3 π r ^{3}

[Formula.]

Step: 4

= 4 3 π × 12^{3}

Step: 5

= 7234.56 cm^{3}

Correct Answer is : 7234.56 cm^{3}

Step: 1

Curved surface area of the hemisphere = 2π r ^{2}

Volume of the hemisphere =2 3 π r ^{3}

Volume of the hemisphere =

[Formula]

Step: 2

Curved surface area of the hemisphere = volume of the hemisphere

[According to the data given]

Step: 3

2πr ^{2} = 2 3 πr ^{3}

[Substitute]

Step: 4

Step: 5

Correct Answer is : 56.52 cubic units

Step: 1

Volume of the sphere = 4 3 π r ^{3}

[Formula]

Step: 2

Volumes of three hemispheres = 2 3 π (5)^{3} + 2 3 π (6)^{3} + 2 3 π (4)^{3} [Volume of the hemisphere

=2 3 π (r ^{3}).]

=

Step: 3

As the sphere is formed by melting three hemispheres, volume of the sphere is equal to the volumes of three hemispheres.

Step: 4

Step: 5

Correct Answer is : r = 2 0 2 . 5 3 units

Step: 1

Volume of one sphere = 4 3 × 3 × (3^{3}) = 108 cm^{3}

[Volume of the sphere = 4 3 π (r ^{3}).]

Step: 2

Volume of 15 spheres = 15 × 108 = 1620 cm^{3}

[Multiply.]

Step: 3

Volume of water in the jar = 3 × (20^{2}) × 30 = 36000 cm^{3}

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

Step: 4

Total volume of water + balls(V) ⇒ 1620 + 36000 = 37620 cm^{3}

[Simplify.]

Step: 5

Volume of the water in the cylinder when spherical balls are immersed = 37620 cm^{3}

[From step 4.]

Step: 6

[From step 5.]

Step: 7

Height to which water is filled in the jar ⇒
3 7 6 2 0 3 × ( 2 0 ) ² = 31.35 cm

Correct Answer is : 31.35 cm

Step: 1

Volume of the cone = 1 3 × 3 × (2^{2}) 7
= 28 cm³

[Volume of the cone = 1 3 π (r ^{2}) h .]

Step: 2

Volume of the sphere = 4 3 × 3 × (2^{3})
= 32 cm^{3}

[Volume of a sphere = 4 3 π (r )^{3}.]

Step: 3

Sum of the volumes = 28 + 32 = 60 cm^{3}

[Simplify.]

Correct Answer is : 60 cm³

Step: 1

Number of bottles required = total volume of the liquid volume of one bottle

[Formula.]

Step: 2

Volume of the liquid = Volume of the hemisphere ⇒ 2 3 × 3 × 120^{3} = 3456000 cm^{3}

[Volume of the hemisphere = 2 3 π r ^{3}.]

Step: 3

Volume of one bottle ⇒ 3 × (3)^{2} × 6 = 162 cm^{3}

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

Step: 4

Number of bottles ⇒ 3456000 162 = 21333.33 (approximately)

[From steps 2 and 3.]

Correct Answer is : 21333

Step: 1

Radius of the tank = 3 m

[Given.]

Step: 2

Volume of the tank = 2 3 × 3 × (3)^{3} × 1000 litres
= 54000 litres

[Volume of the tank = 2 3 π r ^{3}.]

[1 m^{3} = 1000 litres.]

[1 m

Step: 3

Rate of filling the water = 4 litres/sec,

[Given.]

Step: 4

Time taken to fill the tank = Volume of the tank rate of filling

[Formula.]

Step: 5

Time taken to fill the tank = 54000 4

= 13500 seconds = 225 min

= 13500 seconds = 225 min

[Simplify.]

[1 minute = 60 seconds.]

[1 minute = 60 seconds.]

Correct Answer is : 225 min

[Round your answer to nearest whole number and take

Step: 1

Nuumber of spherical balls made = Total volume of lead volume of one spherical ball

[Formula.]

Step: 2

Total volume of lead = 40 cm × 50 cm × 60 cm ⇒ 120000 cm^{3}

[Given.]

Step: 3

Volume of one spherical ball = 4 3 × 3 × (2)³ ⇒ 32 cm³

[Volume of a sphere = 4 3 π r ^{3}.]

Step: 4

Number of spherical balls = 120000 32 ⇒ 3750 (approximately)

[Simplify.]

Correct Answer is : 3750

Step: 1

Length of the iron rod = Volume of the rod base area

[Formula.]

Step: 2

Volume of each sphere = 4 3 × 3 × (1.5)^{3} ⇒ 13.50 inches^{3}

[Volume of the sphere = 4 3 π r ^{3}.]

Step: 3

Volume of five spheres = 5 × 13.50 ⇒ 67.50 inches^{3}

[From step 2.]

Step: 4

Base area of the rod = 3 × (0.5) 2 4 = 0.1875 inches^{2}

[Base area of the rod = π d ² 4 .]

Step: 5

Length of the rod = 67.50 0.1875 = 360 inches = 9.14 m

[Substitute in step1 and simplify.]

[1 inch = 0.0254 meter.]

[1 inch = 0.0254 meter.]

Correct Answer is : 9.14 m

Step: 1

Radius of the sphere = radius of the cone = r

[Given.]

Step: 2

Volume of the sphere = 4 3 πr ^{3}

[Formula.]

Step: 3

Volume of the cone = 1 3 πr ^{2}h

[Formula.]

Step: 4

Volume of the sphere = 2 × Volume of the cone

[Given.]

Step: 5

[Substitute and simplify.]

Step: 6

Therefore, h = 2r .

Correct Answer is : h = 2r

Step: 1

Surface area of the sphere = 4π r ^{2}

Step: 2

Volume of the sphere = 4 3 π r ^{3}

[Formula]

Step: 3

Surface area of the sphere = volume of the sphere

[According to the data given]

Step: 4

4π r ^{2} = 4 3 π r ^{3}

[Substitute]

Step: 5

Step: 6

Volume of sphere = 4 3 π (3)^{3} = 113.04 cubic units.

Correct Answer is : 113.04 cubic units

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