Respuesta :
Answer:
height of the cone = 4.01273885 units
Step-by-step explanation:
Volume of a cone(V) is given by:
[tex]V = \frac{1}{3} \pi r^2h[/tex] ....[1]
where,
r is the radius and h is the height of the cone.
As per the statement:
A cone with radius 5 units and ts volume is 105 cubic units
⇒r = 5 units and V = 105 cubic units
Substitute these given values and use [tex]\pi = 3.14[/tex] in [1] we have;
[tex]105 = \frac{1}{3} \cdot 3.14 \cdot 5^2 \cdot h[/tex]
Multiply both sides by 3 we have;
⇒[tex]315 = 78.5 \cdot h[/tex]
Divide both sides by 78.5 we have;
[tex]4.01273885 = h[/tex]
or
h = 4.01273885 units
Therefore, the height of the cone is, 4.01273885 units
The height of the cone is 4 units.
What is the volume of a cone?
The volume of the cone is equal to;
[tex]\rm Volume \ of \ cone=\dfrac{1}{3} \times b \times h[/tex]
Where; B is the area of the circular base of the cone, and h is the height of the cone.
The base of the cone is given by;
[tex]\rm Base=\pi r^2[/tex]
Substitute all the values in the equation
[tex]\rm Volume \ of \ cone=\dfrac{1}{3} \times b \times h\\\\Volume \ of \ cone=\dfrac{1}{3} \times \pi r^2\times h \\\\ 105=\dfrac{1}{3} \times 3.14 \times 5^2\times h\\\\h = \dfrac{105\times 3}{25 \times 3.14}\\\\h=64[/tex]
Hence, the height of the cone is 4 units.
To know more about cone click the link given below.
https://brainly.com/question/12445166
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