Asked by Cooper P smith
A dump truck pours sand into a container in the shape of a rectangular prism with a square base of length 2 feet. The height, h , of the sand in the container increases at a rate of approximately 8 inches per minute. Create an equation that models the volume, V , of the sand in the container in terms of h , then use the equation to determine the time at which the volume is 64 cubic feet. Note that the volume of a rectangular prism is V=l×w×h , where l , w , and h are the length, width, and height of the prism.
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Answer
is that correct?
Answered by
GPT 3.5
The length and width of the container's base are both 2 feet, so the area of the base is 2 * 2 = 4 square feet. Since the height of the sand is h feet, the volume of the sand in the container is V = 4 * h cubic feet.
To determine the time at which the volume is 64 cubic feet, we need to solve the equation 4 * h = 64 for h.
Dividing both sides of the equation by 4, we get h = 64 / 4 = 16 feet.
So the volume of the sand is 64 cubic feet when the height is 16 feet. We can use this to determine the time it takes for the height to reach 16 feet.
Since the height is increasing by 8 inches per minute, we can convert 16 feet to inches (16 * 12 = 192 inches) and divide by the rate of increase (192 / 8 = 24 minutes).
Therefore, the volume of the sand is 64 cubic feet when the time is 24 minutes.
To determine the time at which the volume is 64 cubic feet, we need to solve the equation 4 * h = 64 for h.
Dividing both sides of the equation by 4, we get h = 64 / 4 = 16 feet.
So the volume of the sand is 64 cubic feet when the height is 16 feet. We can use this to determine the time it takes for the height to reach 16 feet.
Since the height is increasing by 8 inches per minute, we can convert 16 feet to inches (16 * 12 = 192 inches) and divide by the rate of increase (192 / 8 = 24 minutes).
Therefore, the volume of the sand is 64 cubic feet when the time is 24 minutes.
Answered by
GPT 3.5
Apologies for the mistake in my previous response. Let's go through the problem correctly:
The length and width of the container's base are both 2 feet, so the area of the base is 2 * 2 = 4 square feet. Since the height of the sand is h feet, the volume of the sand in the container is V = 4 * h cubic feet.
Therefore, the equation that models the volume of the sand in terms of h is V = 4h.
To determine the time at which the volume is 64 cubic feet, we need to find the value of h when V = 64. Plugging in this value, we get 64 = 4h.
Dividing both sides of the equation by 4, we get h = 16.
Since the height is increasing at a rate of 8 inches per minute, we need to convert 16 feet to inches (16 * 12 = 192 inches). Dividing by the rate of increase (192 / 8 = 24 minutes), we find that it takes 24 minutes for the height to reach 16 feet.
Therefore, the volume of the sand is 64 cubic feet when the time is 24 minutes.
The length and width of the container's base are both 2 feet, so the area of the base is 2 * 2 = 4 square feet. Since the height of the sand is h feet, the volume of the sand in the container is V = 4 * h cubic feet.
Therefore, the equation that models the volume of the sand in terms of h is V = 4h.
To determine the time at which the volume is 64 cubic feet, we need to find the value of h when V = 64. Plugging in this value, we get 64 = 4h.
Dividing both sides of the equation by 4, we get h = 16.
Since the height is increasing at a rate of 8 inches per minute, we need to convert 16 feet to inches (16 * 12 = 192 inches). Dividing by the rate of increase (192 / 8 = 24 minutes), we find that it takes 24 minutes for the height to reach 16 feet.
Therefore, the volume of the sand is 64 cubic feet when the time is 24 minutes.
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