A conical flask with radius 10 cm and height of 15 cm is half full of water. A stone was placed inside
and water rose to of the flask. Find the volume of the stone to 3 s.f.

Question

A conical flask with radius 10 cm and height of 15 cm is half full of water. A stone was placed inside and water rose to $$ 3 / 4 $$ of the flask. Find the volume of the stone to 3 s.f.

UpStudy AI · Accepted Answer

To find the volume of the stone, we need to calculate the volume of water that rose when the stone was placed inside the conical flask.

Given:
- Radius of the conical flask, $$ r = 10 \, \text{cm} $$
- Height of the conical flask, $$ h = 15 \, \text{cm} $$
- Water rose to $$ \frac{3}{4} $$ of the flask

The volume of water that rose can be calculated using the formula for the volume of a cone:
$$ V = \frac{1}{3} \pi r^2 h $$

Since the water rose to $$ \frac{3}{4} $$ of the flask, the volume of water that rose is:
$$ V_{\text{water}} = \frac{3}{4} \times \frac{1}{3} \pi r^2 h $$

Now, we need to find the volume of the stone. The volume of the stone is equal to the volume of water that rose minus the volume of water that was initially in the flask.

The volume of water that was initially in the flask is half the volume of the flask:
$$ V_{\text{initial water}} = \frac{1}{2} \times \frac{1}{3} \pi r^2 h $$

Therefore, the volume of the stone is:
$$ V_{\text{stone}} = V_{\text{water}} - V_{\text{initial water}} $$

Let's calculate the volume of the stone.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{3}{4}\times \frac{1}{3}\pi \times 10^{2}\times 15-\frac{1}{2}\times \frac{1}{3}\pi \times 10^{2}\times 15$$
- step1: Multiply:
  $$375\pi -\frac{1}{2}\times \frac{1}{3}\pi \times 10^{2}\times 15$$
- step2: Multiply:
  $$375\pi -250\pi $$
- step3: Collect like terms:
  $$\left(375-250\right)\pi $$
- step4: Subtract the numbers:
  $$125\pi $$
The volume of the stone is approximately 392.7 cm³ to 3 significant figures.
The volume of the stone is approximately 393 cm³.

A conical flask with radius 10 cm and height of 15 cm is half full of water. A stone was placed inside
and water rose to of the flask. Find the volume of the stone to 3 s.f.

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A conical flask with radius 10 cm and height of 15 cm is half full of water. A stone was placed inside and water rose to of the flask. Find the volume of the stone to 3 s.f.

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A conical flask with radius 10 cm and height of 15 cm is half full of water. A stone was placed inside
and water rose to of the flask. Find the volume of the stone to 3 s.f.