Question

A cone with radius 5 units is shown below. Its volume is 105 cubic units. Find the height of the cone.

Answer 1

Answer:

height of the cone  = 4.01273885 units

Step-by-step explanation:

Volume of a cone(V) is given by:

$V = \frac{1}{3} \pi r^2h$             ....[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 $\pi = 3.14$ in [1] we have;

$105 = \frac{1}{3} \cdot 3.14 \cdot 5^2 \cdot h$

Multiply both sides by 3 we have;

⇒$315 = 78.5 \cdot h$

Divide both sides by 78.5 we have;

$4.01273885 = h$

or

h = 4.01273885 units

Therefore, the height of the cone is, 4.01273885 units

Answer 2

The height of the cone is 4 units.

What is the volume of a cone?

The volume of the cone is equal to;

$\rm Volume \ of \ cone=\dfrac{1}{3} \times b \times h$

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;

$\rm Base=\pi r^2$

Substitute all the values in the equation

$\rm Volume \ of \ cone=\dfrac{1}{3} \times b \times h\\\\Volume \ of \ cone=\dfrac{1}{3} \times \pi r^2\times h \\\\ 105=\dfrac{1}{3} \times 3.14 \times 5^2\times h\\\\h = \dfrac{105\times 3}{25 \times 3.14}\\\\h=64$

Hence, the height of the cone is 4 units.

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https://brainly.com/question/12445166

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