Find the volume of the figure. The diameter of the base is 4 cm. The figure is a cylinder that has d = 4 cm and h = 2.5 with a hemisphere on the top that has the same diameter as the cylinder (4 cm).

Solution:

Given, the figure represents a cylinder with a hemisphere on the top that has the same diameter as the cylinder.

We have to find the volume of the figure.

Total volume = volume of cylinder + volume of hemisphere

Volume of cylinder = πr²h

Where, r is the radius

h is the height of the cylinder

Volume of hemisphere = (2/3)πr³

Where, r is the radius of the hemisphere

Considering cylinder,

Diameter = 4 cm

Radius = 4/2 = 2 cm

Height = 2.5 cm

Volume = π(2)²(2.5)

= π(4)(2.5) = 10π cm³

Considering hemisphere,

Diameter = 4 cm

Radius = 4/2 = 2 cm

Volume = (2/3)π(2)³

= 16π/3 cm³

Now, total volume = 10π + 16π/3

= π(10 + 16/3)

= π(30+16)/3

= 46π/3 cm³

Therefore, the required volume is 46π/3 cm³.

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Find the volume of the figure. The diameter of the base is 4 cm. The figure is a cylinder that has d = 4 cm and h = 2.5 with a hemisphere on the top that has the same diameter as the cylinder (4 cm).

Summary:

The diameter of the base is 4 cm. The figure is a cylinder that has d = 4 cm and h = 2.5 with a hemisphere on the top that has the same diameter as the cylinder (4 cm). The volume of the figure is 46π/3 cm³.