Question

1. radius r = 1/2 diameter = _ cm v = 1/3 bh v = 1/3 (πr²)h v = 1/3 (π×_)×_ v = 1/3 (_)×_ v = _×_ v = v ≈ _ cm³

Explanation:

Step1: Calculate the radius

The diameter is 12 cm. Since $r=\frac{1}{2}d$, then $r = \frac{1}{2}\times12=6$ cm.

Step2: Identify the height

The height $h$ of the cone is 4 cm.

Step3: Substitute values into volume formula

The volume formula of a cone is $V=\frac{1}{3}(\pi r^{2})h$. Substitute $r = 6$ and $h = 4$: $V=\frac{1}{3}(\pi\times6^{2})\times4$.

Step4: Calculate $\pi\times6^{2}$

$6^{2}=36$, so $\pi\times6^{2}=36\pi$. Then $V=\frac{1}{3}(36\pi)\times4$.

Step5: Calculate $\frac{1}{3}\times36\pi$

$\frac{1}{3}\times36\pi = 12\pi$. So $V=12\pi\times4$.

Step6: Calculate the volume

$12\pi\times4 = 48\pi$ $cm^{3}$.

Step7: Approximate the volume

Taking $\pi\approx3.14$, then $V\approx48\times3.14 = 150.72$ $cm^{3}$.

Answer:

$r = 6$; $V=\frac{1}{3}(\pi\times6^{2})\times4$; $V=\frac{1}{3}(36\pi)\times4$; $V = 12\pi\times4$; $V=48\pi$; $V\approx150.72$