Question

1. What is the lateral surface area of a solid 8 meters high

whose base is the figure at right? Dimensions are in meters.
2. Which inequality corresponds to the graph at right?
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Answer 1

Explanation:

To calculate the lateral surface of this shape we must divide it into 3 parts :

• Part 1 : the half cylinder with the radius r=15

We must calculate its perimeter P1 :

P1 = (15*2)*π/2 = 30*π*(1/2)=15π

• Part 2 : the half cylinder with the radius r=12-5=7

We must calculate its perimeter P2:

P2= (7*2)*π/2=14*π*(1/2)= 7π

• Part 3 : the cube

We won't calculate its perimeter because it has some common sides with the cylinders .

Let P3 be the perimeter of what's remaining from the cube

P3=12+5= 17

Now the total perimeter : Pt

Pt= 15π+7π+17= 22π+17

The lateral surface : Ls

Ls= (22π+29)*8= 784.92 m²

• The inequality : -1<x≤4