Question

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

Answer 1

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 = $\frac{52}{2}=26$ cm

And the radius of 1 semi circle is = $\frac{26}{2}=13$ cm

So, area of a complete circle becomes = $\pi r^{2}$

= $3.14\times13\times13=530.66$ 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 = $length \times width$

= $52\times23=1196$ 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 = $0.172666\times470=81.153$ grams.

Answer 2

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