Question

The height of a cone is twice the radius of its base.
What expression represents the volume of the cone, in cubic
units?
1. 2/3 pix^3
2. 4/3 pix^2
3. 2pix^3
4.4pi x^3​

Answer 1

Answer:

The correct answer is option 1. $\frac{2}{3} \pi x^3$ cubic units.

Step-by-step explanation:

The formula for the volume, V of a right angled cone is given as:

$V = \dfrac{1}{3} \pi r^{2} h ...... (1)$

Where, $\pi = 3.14$

$r$ is the radius of the circular base of the cone.

$h$ is the height of the cone.

We are given that height is twice of the radius of its base.

Let the radius of base = $x$ units

Now, As per the question statement,

The height of cone= $2 \times x$ units

Putting the values of $r, h$ in equation (1) to find the volume:

$\Rightarrow \dfrac{1}{3} \times \pi \times x^{2} \times 2x\\\Rightarrow \dfrac{2}{3}\pi x^{3}$

Hence, the correct answer is option 1. $\dfrac{2}{3}\pi x^{3}$ cubic units.