Question

this is a side view of a sluice gate used for letting water into the hydroelectric plant.
1 what is the perimeter of this side view of the sluice gate?
a. 20 ft
b. 28 ft
c. 32 ft
d. 40 ft
2 the sluice gate is 20 feet tall. what is the volume of the sluice gate?
a. 200 ft³
b. 280 ft³
c. 320 ft³
d. 400 ft³
3 the total volume of the white and black rectangular prisms below is 60 cubic units
what is the volume of the white rectangular
a. 40 cubic units
b. 42 cubic units
c. 51 cubic units

Explanation:

Step1: Calculate the perimeter of the sluice gate

The figure can be considered as a composite shape. The perimeter is calculated by adding up all the outer - side lengths.
The lengths of the sides are \(14 + 6+2 + 1+(14 - 6)+(2 - 1)\)

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Step2: Calculate the volume of the sluice gate

The sluice gate can be divided into two rectangular prisms. First, find the area of the cross - section (the side - view area). The side - view area \(A=(14\times1)+(6\times2)=14 + 12=20\) square feet.
The volume \(V=\text{cross - sectional area}\times\text{height}\). Given the height \(h = 20\) feet. So \(V=20\times20 = 400\) cubic feet.

Step3: Calculate the volume of the white rectangular prism

The volume of a rectangular prism is \(V=l\times w\times h\). For the black rectangular prism, \(l = 3\), \(w = 3\), \(h = 2\), so \(V_{black}=3\times3\times2=18\) cubic units.
Since the total volume \(V_{total}=V_{white}+V_{black}\), and \(V_{total}=60\) cubic units. Then \(V_{white}=V_{total}-V_{black}\)

$$V_{white}=60 - 18=42$$

Answer:

1. D. \(40\) ft
2. D. \(400\) ft³
3. B. \(42\) cubic units