To find the volume of the cylinder, we need to know the radius and the height.

1. First, we find the radius. In triangle ABC, since angle BAC = 60° and AC = 3 cm, we can use the properties of a 30-60-90 triangle to find AB (the diameter). In a 30-60-90 triangle, the side opposite the 60° angle (which is AB in this case) is equal to the length of the hypotenuse (AC) times the square root of 3 divided by 2. So, AB = AC * √3 / 2 = 3 * √3 / 2 = √3 * 1.5 cm. Since AB is the diameter, the radius (r) is half of this, so r = √3 * 1.5 / 2 = √3 * 0.75 cm.

2. Next, we find the height. In triangle ABC, BC is the height of the cylinder. Since triangle ABC is a right triangle and angle BAC = 60°, angle ABC = 90° - 60° = 30°. In a 30-60-90 triangle, the side opposite the 30° angle (which is BC in this case) is half the length of the hypotenuse (AC). So, BC = AC / 2 = 3 / 2 = 1.5 cm.

3. Finally, we find the volume. The volume V of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height. Substituting the values we found, V = π * (√3 * 0.75)² * 1.5 = π * (3 * 0.75²) * 1.5 = π * (3 * 0.5625) * 1.5 = π * 1.6875 * 1.5 = π * 2.53125 cm³.

So, the volume of the cylinder is 2.53125π cm³.

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To find the volume of the cylinder, we need to know the radius and the height.

1. First, we find the radius. In triangle ABC, since angle BAC = 60° and AC = 3 cm, we can use the properties of a 30-60-90 triangle to find AB (the diameter). In a 30-60-90 triangle, the side opposite the 60° angle (which is AB in this case) is equal to the length of the hypotenuse (AC) times the square root of 3 divided by 2. So, AB = AC * √3 / 2 = 3 * √3 / 2 = √3 * 1.5 cm. Since AB is the diameter, the radius (r) is half of this, so r = √3 * 1.5 / 2 = √3 * 0.75 cm.

2. Next, we find the height. In triangle ABC, BC is the height of the cylinder. Since triangle ABC is a right triangle and angle BAC = 60°, angle ABC = 90° - 60° = 30°. In a 30-60-90 triangle, the side opposite the 30° angle (which is BC in this case) is half the length of the hypotenuse (AC). So, BC = AC / 2 = 3 / 2 = 1.5 cm.

3. Finally, we find the volume. The volume V of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height. Substituting the values we found, V = π * (√3 * 0.75)² * 1.5 = π * (3 * 0.75²) * 1.5 = π * (3 * 0.5625) * 1.5 = π * 1.6875 * 1.5 = π * 2.53125 cm³.

So, the volume of the cylinder is 2.53125π cm³.

Knowee AI · Accepted Answer

To find the volume of the cylinder, we need to know the radius and the height.

1. First, we find the radius. In triangle ABC, since angle BAC = 60° and AC = 3 cm, we can use the properties of a 30-60-90 triangle to find AB (the diameter). In a 30-60-90 triangle, the side opposite the 60° angle (which is AB in this case) is equal to the length of the hypotenuse (AC) times the square root of 3 divided by 2. So, AB = AC * √3 / 2 = 3 * √3 / 2 = √3 * 1.5 cm. Since AB is the diameter, the radius (r) is half of this, so r = √3 * 1.5 / 2 = √3 * 0.75 cm.

2. Next, we find the height. In triangle ABC, BC is the height of the cylinder. Since triangle ABC is a right triangle and angle BAC = 60°, angle ABC = 90° - 60° = 30°. In a 30-60-90 triangle, the side opposite the 30° angle (which is BC in this case) is half the length of the hypotenuse (AC). So, BC = AC / 2 = 3 / 2 = 1.5 cm.

3. Finally, we find the volume. The volume V of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height. Substituting the values we found, V = π * (√3 * 0.75)² * 1.5 = π * (3 * 0.75²) * 1.5 = π * (3 * 0.5625) * 1.5 = π * 1.6875 * 1.5 = π * 2.53125 cm³.

So, the volume of the cylinder is 2.53125π cm³.

Here is a cylinder.AB is a diameter of the circular face and BC is the height of the cylinder.Triangle ABC is a right-angled triangle with angle BAC = 60° and AC = 3 cmWork out the volume of the cylinder giving your answer in terms of π

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