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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.

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 o class=

Answer :

Ashraf82

Answer:

The hat weight = 81.166 g

Step-by-step 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

Answer:

Weight of fabric is = 81.153 grams.

Step-by-step 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 = [tex]\frac{52}{2}=26[/tex] cm

And the radius of 1 semi circle is = [tex]\frac{26}{2}=13[/tex] cm

So, area of a complete circle becomes = [tex]\pi r^{2}[/tex]

= [tex]3.14\times13\times13=530.66[/tex] cm square

For area of rectangle we need the width.

The radius is 13 so the width of rectangle will be = [tex]36-13=23[/tex] cm

Now area of rectangle is = [tex]length \times width[/tex]

= [tex]52\times23=1196[/tex] cm square

Total area is = [tex]1196+530.66[/tex] = 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 = [tex]0.172666\times470=81.153[/tex] grams.

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