Question

100 POINTS

Find the volume of the composite solid.

A ) 1099.01 m^3

B) 104.67 m^3

C) 889.67 m^3

D) 785 m^3

Answer 1

`\textsf{C)}\quad \sf 889.67\: m^3`

Explanation:

The given composite solid is made up of a cylinder and a cone.

To find the volume of the composite solid, find the volume of the cylinder and the volume of the cone, then add them together.

Volume of a cylinder:

`\sf V=\pi r^2 h`

(where r is the radius and h is the height)

Given:

• r = 5 m
• h = 10 m

Substitute the given values into the formula and solve for V:

`\begin{aligned}\implies \sf Volume\:of\:the\:cylinder & = \sf \pi (5)^2(10)\\ & = \sf 250 \pi \:\:m^3 \end{aligned}`

Volume of a cone:

`\sf V=(1)/(3) \pi r^2 h`

(where r is the radius and h is the height)

Given:

• r = 5 m
• h = 4 m

Substitute the given values into the formula and solve for V:

`\begin{aligned}\implies \sf Volume\:of\:the\:cone & = \sf (1)/(3) \pi (5)^2(4)\\ & = \sf (100)/(3)\pi \:\:m^3 \end{aligned}`

Therefore, the volume of the composite solid is:

`\begin{aligned}\implies \sf Volume\:of\:composite\:solid & = \sf Cylinder\:volume+Cone\:volume\\ & = \sf 250\pi + (100)/(3)\pi \\ & = \sf (850)/(3) \pi \\ & = \sf (850)/(3) * 3.14 \\ & = \sf 889.67\:m^3\:(2\:d.p.)\end{aligned}`

Answer 2

Volume of a cylinder: PI x radius^2 x height

= 3.14 x 5^2 x 10 = 785 m^3

Volume of a cone: pi x radius^2 x height/3

= 3.14 x 5^2 x 4/3 = 104.67 m^3

Total volume = 785 + 104.67 = 889.67 M63

Answer: C. 889.67 M^3