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A bucket is 12cm in diameter at the top 8cm in diameter at the bottom and 4cm deep.
Calculate it's volume (in cm^3 in terms of π)?
Anonymous
more than 1 week ago
A bucket is 12cm in diameter at the top 8cm in diameter at the bottom and 4cm deep. Calculate it's volume (in cm^3 in terms of π)?
Please 🙏🙏🙏🙏
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ChatGPT
more than 1 week ago
To calculate the volume of the bucket, we need to find the average radius of the top and bottom of the bucket.
Radius of the top of the bucket = 12cm / 2 = 6cm
Radius of the bottom of the bucket = 8cm / 2 = 4cm
Average radius = (6cm + 4cm) / 2 = 5cm
Now, we can calculate the volume of the bucket using the formula for the volume of a frustum of a cone:
V = (1/3)πh(R^2 + r^2 + Rr)
where:
V = volume
h = height = 4cm
R = radius of the top of the bucket = 6cm
r = radius of the bottom of the bucket = 4cm
Plugging in the values:
V = (1/3)π(4)(6^2 + 4^2 + 6*4)
V = (1/3)π(4)(36 + 16 + 24)
V = (1/3)π(4)(76)
V = (4/3)π(76)
V = 304π/3
Therefore, the volume of the bucket is 304π/3 cm^3.
Radius of the top of the bucket = 12cm / 2 = 6cm
Radius of the bottom of the bucket = 8cm / 2 = 4cm
Average radius = (6cm + 4cm) / 2 = 5cm
Now, we can calculate the volume of the bucket using the formula for the volume of a frustum of a cone:
V = (1/3)πh(R^2 + r^2 + Rr)
where:
V = volume
h = height = 4cm
R = radius of the top of the bucket = 6cm
r = radius of the bottom of the bucket = 4cm
Plugging in the values:
V = (1/3)π(4)(6^2 + 4^2 + 6*4)
V = (1/3)π(4)(36 + 16 + 24)
V = (1/3)π(4)(76)
V = (4/3)π(76)
V = 304π/3
Therefore, the volume of the bucket is 304π/3 cm^3.
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Google Gemini AI
more than 1 week ago
The volume of a frustum of a cone is given by:
$$V = \frac{1}{3} \pi h (R^2 + r^2 + Rr)$$
where h is the height of the frustum, R is the radius of the top base, and r is the radius of the bottom base.
In this case, h = 4cm, R = 6cm, and r = 4cm. Substituting these values into the formula, we get:
$$V = \frac{1}{3} \pi (4) ((6)^2 + (4)^2 + (6)(4))$$
$$V = \frac{1}{3} \pi (4) (36 + 16 + 24)$$
$$V = \frac{1}{3} \pi (4) (76)$$
$$V = \frac{304}{3} \pi$$
$$V = 101.33 \pi cm^3$$
$$V = \frac{1}{3} \pi h (R^2 + r^2 + Rr)$$
where h is the height of the frustum, R is the radius of the top base, and r is the radius of the bottom base.
In this case, h = 4cm, R = 6cm, and r = 4cm. Substituting these values into the formula, we get:
$$V = \frac{1}{3} \pi (4) ((6)^2 + (4)^2 + (6)(4))$$
$$V = \frac{1}{3} \pi (4) (36 + 16 + 24)$$
$$V = \frac{1}{3} \pi (4) (76)$$
$$V = \frac{304}{3} \pi$$
$$V = 101.33 \pi cm^3$$
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