Question

this is a side view of a sluice gate used for letting water in 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 10 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 prisms below is 60 cubic units
what is the volume of the white re
a. 40 cubic units
b. 42 cubic units
c. 51 cubic units
d. 57 cubic units

Explanation:

Step1: Calculate the perimeter of the sluice gate

The perimeter of a shape is the sum of all its sides.
For the given sluice - gate side - view:
The lengths of the sides are \(14 + 6+2 + 1+(14 - 6)+(2 - 1)\)
First, simplify the non - straightforward sides: \(14-6 = 8\) and \(2 - 1=1\)
Then sum all the sides: \(14+6 + 2+1+8+1\)
\(14+6=20\), \(20+2 = 22\), \(22+1=23\), \(23+8=31\), \(31+1 = 40\)

Step2: Calculate the volume of the sluice gate

The volume of a composite rectangular - prism (the sluice gate) is calculated by finding the area of the cross - section and multiplying by the height (\(h = 20\) ft).
The cross - section area \(A\) is the sum of the areas of two rectangles.
One rectangle has dimensions \(14\times1\) and the other has dimensions \(6\times2\)
\(A=14\times1+6\times2=14 + 12=26\) square feet
The volume \(V=A\times h\), substituting \(h = 20\)
\(V=26\times20 = 520\) (This part seems to have a wrong height value in the original problem, assuming it's a typo and if the height is \(20\) ft). But if we consider the first - part perimeter problem (maybe a mis - labeled problem set), for the third problem (assuming it's a separate volume problem for two prisms):
The volume of the black prism (a rectangular prism) with \(l = 3\), \(w=3\), \(h = 2\) is \(V_{black}=3\times3\times2=18\) cubic units
If the total volume \(V_{total}=60\) cubic units, then the volume of the white prism \(V_{white}=V_{total}-V_{black}\)
\(V_{white}=60 - 18=42\) cubic units

Answer:

1. D. \(40\) ft
2. (Assuming height \(h = 20\) ft for the sluice - gate volume, but if it's a mis - labeled problem, for the third problem) B. \(42\) cubic units