1.) The first person who requires your assistance is Tina the bearded lady. Tina’s side job is to look after the elephants (she double majored at circus university.)
a. Tina must fill the semi-circular trough shown above with peanuts. Tina knows that the store bought peanuts she can buy will each fill up 1.5 ft3. How many bags of peanuts should she buy to fill up the 12 troughs? [3 marks]
b. Tina notices that the trapezoid shaped water trough has sprung a leak. If the leak drains at a rate of 1.37ft3/s how long until the trough empties (the hole is in the bottom of the trough?) [3 marks]
a. To find out how many bags of peanuts Tina should buy to fill up the 12 troughs, we need to calculate the total volume of the troughs and then divide it by the volume of one bag of peanuts.
Given that each bag of peanuts can fill up 1.5 ft^3, we need to find the total volume of the 12 troughs. Since the troughs are semi-circular, we can use the formula for the volume of a semi-circular shape, which is (1/2) * π * r^2 * h.
However, we need to know the radius (r) and height (h) of the troughs to calculate the volume. Please provide this information to proceed with the calculation.
b. To determine how long it will take for the trapezoid-shaped water trough to empty due to the leak, we need to calculate the time based on the rate of drainage.
Given that the leak drains at a rate of 1.37 ft^3/s, we need to find the volume of the trough and divide it by the rate of drainage to get the time taken.
To calculate the volume of the trapezoid-shaped trough, we can use the formula for the volume of a trapezoidal prism, which is (1/2) * (a + b) * h * L, where a and b are the lengths of the parallel sides, h is the height, and L is the length of the trough.
However, we need to know the values of a, b, h, and L to perform the calculation. Please provide this information to proceed with the calculation.