Question

Which expression represents the volume, in cubic units, of the composite figure?

Answer 1

The missing figure is attached

The expression represents the volume in cubic units of the composite figure is (Four-third)π(10)³ + π(10)²(28) ⇒ 1st answer

Step-by-step explanation:

The figure consists of

• Two hemispheres
• A cylinder

The volume of the hemisphere = $\frac{2}{3}\pi r^{3}$ , where r is its radius

The volume of the cylinder = πr²h, where r is its radius and h is its height

∵ The diameter of the hemisphere s and the cylinder is 20 units

∵ The radius = $\frac{1}{2}$ diameter

∴ The radius = $\frac{1}{2}$ × 20 = 10 units

∵ The volume of a hemisphere = $\frac{2}{3}$ πr³

∵ r = 10

- Substitute r by 10 in the rule

∴ The volume of a hemisphere = $\frac{2}{3}$ π(10)³

∵ The volume of the cylinder = πr²h

∵ h = 28 and r = 10

- Substitute h by 28 and r by 10 in the rule

∴ The volume of the cylinder = π(10)²(28)

∵ The volume of the figure = 2(volume of a hemisphere) +

   volume of the cylinder

∴ The volume of the figure = 2( $\frac{2}{3}$ )π(10)³ + π(10)²(28)

∵ 2 × $\frac{2}{3}$ = $\frac{4}{3}$

∴ The volume of the figure = $\frac{4}{3}$ π(10)³ + π(10)²(28)

The expression represents the volume in cubic units of the composite figure is (Four-third)π(10)³ + π(10)²(28)

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Answer 2

Answer:

A

Step-by-step explanation: