Question

Find the volume of a right circular cone \[1.02\] m high, if the radius of its base is 28 cm.
A) \[83776{\rm{c}}{{\rm{m}}^3}\]
B) \[73676{\rm{c}}{{\rm{m}}^3}\]
C) \[82546{\rm{c}}{{\rm{m}}^3}\]
D) \[82776{\rm{c}}{{\rm{m}}^3}\]

Answer 1

Hint:
We will first convert the height of the given right circular cone into centimetres. Then, we will substitute the given dimensions in the formula of the volume of a right circular cone to find the required volume.

Formula used:
Volume of a right circular cone, \[V = \dfrac{1}{3}\pi {r^2}h\], where \[r\] is the radius if the cone and \[h\] is the height of the cone.

Complete step by step solution:
In the problem, it is given the height of the right circular cone, \[h = 1.02\] m and the radius of the cone is \[r = 28\] cm.

Let us convert the height into centimetres. We know that 1 m \[ = 100\] cm
So, \[1.02\] m \[ = 1.02 \times 100 = 102\] cm
Let us substitute the given values in the formula for volume of a right circular cone, \[V = \dfrac{1}{3}\pi {r^2}h\]. We have
\[V = \dfrac{1}{3} \times \dfrac{{22}}{7} \times {(28)^2} \times 102\]
Applying the exponent on the term, we get
\[ \Rightarrow V = \dfrac{1}{3} \times \dfrac{{22}}{7} \times 784 \times 102\]
Multiplying the terms, we get
\[ \Rightarrow V = 83776{\rm{c}}{{\rm{m}}^3}\]
Therefore, we get the volume of the right circular cone as \[83776{\rm{c}}{{\rm{m}}^3}\].

Thus, option A is the correct answer.

Note:
We should not get confused between The slant height (\[l\]) of a right circular cone and its vertical height (\[h\]). The slant height (\[l\]) is the distance from any point on the circle of its base to the vertex of the cone, whereas the vertical height (\[h\]) is the perpendicular distance from the midpoint of the circular base to the vertex of the cone. In the given problem, we have assumed \[\pi = \dfrac{{22}}{7}\]. This value of \[\pi \] is more convenient to use when any of the parameters in the formula (i.e., radius, height, slant height, etc.) is a multiple of 7.