Answer:
[tex]\textsf{C)}\quad \sf 889.67\: m^3[/tex]
Step-by-step 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:
[tex]\sf V=\pi r^2 h[/tex]
(where r is the radius and h is the height)
Given:
Substitute the given values into the formula and solve for V:
[tex]\begin{aligned}\implies \sf Volume\:of\:the\:cylinder & = \sf \pi (5)^2(10)\\ & = \sf 250 \pi \:\:m^3 \end{aligned}[/tex]
Volume of a cone:
[tex]\sf V=\dfrac{1}{3} \pi r^2 h[/tex]
(where r is the radius and h is the height)
Given:
Substitute the given values into the formula and solve for V:
[tex]\begin{aligned}\implies \sf Volume\:of\:the\:cone & = \sf \dfrac{1}{3} \pi (5)^2(4)\\ & = \sf \dfrac{100}{3}\pi \:\:m^3 \end{aligned}[/tex]
Therefore, the volume of the composite solid is:
[tex]\begin{aligned}\implies \sf Volume\:of\:composite\:solid & = \sf Cylinder\:volume+Cone\:volume\\ & = \sf 250\pi + \dfrac{100}{3}\pi \\ & = \sf \dfrac{850}{3} \pi \\ & = \sf \dfrac{850}{3} \times 3.14 \\ & = \sf 889.67\:m^3\:(2\:d.p.)\end{aligned}[/tex]
