Exercise 111 Page 574

a When watching the solid from the front, right, and top, it would look like below.

b Each of the cubes has a side length of 1 unit. Therefore, each side of each cube must have a surface area of 1 unit^2. To find the total surface area of the solid, we will count the number of cube sides we can see from the front, left, right, top, and bottom of the solid.

In total, we have 42 cube sides that we can see from the front, right, top, back, left, and bottom. Since there are no hidden cubes, the surface area is 42 square units. To find volume, remember that each cube has a side of 1 unit, so every cube has a volume of (1)(1)(1)=1 cube (1^3) units. The solid has 12 cubes, which means the volume is 12 cube units.

c From Part B, we know that the solid has a volume of 12 units^3. If any of the nets have the same volume, the product of the width, length and height must equal 12 units^3 as well. Let's identify these dimensions for the three nets.

By multiplying the dimensions, we can find the volume of each box. i.& V=(3)(2)(2)=12 units^3 ii.& V=(1)(4)(3)=12 units^3 iii.& V=(2)(2)(3)=12 units^3 All of the nets have the same volume as the solid when turned into a box.

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Exercise 111 Page 574

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