Question

A beanie hat is to be made from a piece of fabric and one square metre of this fabric weighs 470g.

The diagram shows the pattern for the beanie hat consisting of two identical semi-circles attached to a rectangle. How much will the fabric in this beanie hat weigh? Give your answer in grams.

Answer 1

Weight of fabric is = 81.153 grams.

Explanation:

The given diagram has two identical semi-circles attached to a rectangle.

So, we will find the area of the two semi circles or a circle plus the area of rectangle.

Now, the length of the rectangle is = 52 cm

And looking at the above portion, we can say that 2 diameters are 52 cm

1 diameter will be =
`(52)/(2)=26` cm

And the radius of 1 semi circle is =
`(26)/(2)=13` cm

So, area of a complete circle becomes =
`\pi r^(2)`

=
`3.14*13*13=530.66` cm square

For area of rectangle we need the width.

The radius is 13 so the width of rectangle will be =
`36-13=23` cm

Now area of rectangle is =
`length * width`

=
`52*23=1196` cm square

Total area is =
`1196+530.66` = 1726.66 cm square

Now we will convert this in meter square.

1 cm square = 0.0001 meter square

1726.66 cm square = 0.172666 meter square

Weight of 1 meter square fabric = 470 grams

Therefore, weight of 0.172666 meter square fabric is =
`0.172666*470=81.153` grams.

Answer 2

The hat weight = 81.166 g

Explanation:

∵The figure formed by a rectangle and two identical semi-circle

∵ The length of the rectangle = 52 cm = 0.52 m

∴ The length of the two diameter = 52 cm = 0.52 m

∴ The radius of the semi-circle = 52 ÷ 4 = 13 cm = 0.13 m

∴ The width of the rectangle = 36 - 13 = 23 cm = 0.23 m

∴ The area of the rectangle = 0.52 × 0.23 = 0.1196 m²

∴ The area of the semi-circles = π (0.13)² = 0.0531 m²

∴ The area of the hat = 0.1196 + 0.0531 = 0.17269292 m²

∵ 1 m² = 470 g

∴ The weight of the hat = 0.17269292 × 470 = 81.16567 ≅ 81.166 g