Question

The volume of the cone whose vertical height \[{\text{8m}}\] is and the area of the base is \[156{m^2}\] is
A.\[{\text{416}}{{\text{m}}^{\text{3}}}\]
B.\[{\text{415}}{{\text{m}}^{\text{3}}}\]
C.\[{\text{312}}{{\text{m}}^{\text{3}}}\]
D.\[{\text{468}}{{\text{m}}^{\text{3}}}\]

Answer 1

Hint: \[V = \dfrac{1}{3}\pi {r^2}h\] is the formula to calculate the volume of cones. And here the base area and height of the triangle are known and so the volume of can be easily calculated.

Complete step-by-step answer:
The base area is \[156{m^2}\]and height is \[{\text{8m}}\]so,
\[
  {{V = }}\dfrac{{{1}}}{{{3}}}{{\pi }}{{\text{r}}^{\text{2}}}{\text{h}} \\
  {\text{V = }}\dfrac{{\text{1}}}{{\text{3}}}{\text{(basearea)(height)}} \\
  {\text{V = }}\dfrac{{\text{1}}}{{\text{3}}}{\text{(156)(8)}} \\
  {{V = 52 \times 8}} \\
  {\text{V = 416}}{{{m}}^{\text{3}}} \\
\]
Thus , option (a) is our required answer.

Note: A cone is a shape formed by using a set of line segments or the lines which connects a common point, called the apex or vertex, to all the points of a circular base (which does not contain the apex). The distance from the vertex of the cone to the base is the height of the cone.
Properties of Cone
1.A cone has only one face, which is the circular base but no edges.
2.A cone has only one apex or vertex point.
3.Volume of cone is \[V = \dfrac{1}{3}\pi {r^2}h\]
Additional information Cones Around Us:
Cones can be found in a variety of things we see every day. Some examples are mentioned below:
a.A funnel is shaped like a cone.
b.An ice cream is scooped in a conical pastry.
c.The barriers we see on roads are also conical.
d.The birthday hats are conical in shape.