Let's solve for the height $h$ of the cone.

Given:

• Formula for volume of a cone:
  $V = \frac{1}{3} \pi r^2 h$
• Volume: $700$ cm³
• Diameter: $8$ cm (so the radius $r = 4$ cm)

Step 1: Substitute values into the formula

$700 = \frac{1}{3} \pi (4)^2 h$

$700 = \frac{1}{3} \pi (16) h$

$700 = \frac{16\pi h}{3}$

Step 2: Solve for $h$

Multiply both sides by 3:

$2100 = 16\pi h$

Divide by $16\pi$:

$h = \frac{2100}{16\pi}$

$h \approx \frac{2100}{50.24}$

$h \approx 41.8$

Final Answer:

$h \approx 41.8 \text{ cm (to 1 d.p.)}$

Would you like a step-by-step breakdown or further clarification?

Related Questions:

1. How do you derive the formula for the volume of a cone?
2. If the height was doubled, what would the new volume be?
3. What is the surface area of this cone?
4. How does changing the radius affect the volume of a cone?
5. Can the volume of a cone ever be greater than that of a cylinder with the same height and base radius?

Tip:

When working with formulas involving $\pi$, keep intermediate values in terms of $\pi$ to maintain accuracy before rounding at the final step.