Video: Pack 4 • Paper 3 • Question 6

Pack 4 • Paper 3 • Question 6

02:41

Video Transcript

Here is a rectangle and a square. They have the same width. The length of the rectangle is five centimeters longer than its width. Four rectangles and two squares are used to make this net. The perimeter of the 12-sided net is 52 centimeters. Find the volume of the cuboid made when the net is folded.

As the rectangle and the square have the same width, we can let this equal 𝑥. As all four sides of a square are equal, the length of the square will also be equal to 𝑥. As the length of the rectangle is five centimeters longer than its width, an expression for the length would be 𝑥 plus five.

We can now transfer these values onto the diagram of the net. The perimeter of the net would be calculated by adding the lengths of all the sides of the outside of the shape. As the perimeter of the net is 52 centimeters, we know that 12𝑥 plus 𝑥 plus five plus 𝑥 plus five is equal to 52. Grouping the like terms gives us 14𝑥 plus 10 is equal to 52 as 12𝑥 plus 𝑥 plus 𝑥 is equal to 14𝑥 and five plus five is equal to 10. Subtracting 10 from both sides of this equation gives us 14𝑥 is equal to 42. And finally, dividing both sides of this equation by 14 gives us a value for 𝑥 equal to three.

This means that the square has sides of three centimeters and the rectangle has a width of three centimeters and a length of eight centimeters. The question asked us to find the volume of the cuboid when the net is folded. The volume of any cuboid can be calculated by multiplying the three dimensions: the length, the width, and the height. In this case, we need to multiply eight centimeters by three centimeters by three centimeters. Eight multiplied by three is 24 and 24 multiplied by three is 72.

Therefore, the volume of the cuboid is 72 centimeters cubed.

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