Question

In Exercise 4, find the surface area of the solid
formed by the net.

Answer 1

3. 150.72 in²

4. 535.2cm²

Explanation:

3. The solid formed by the net given in problem 3 is the net of a cylinder.

The cylinder bases are the 2 circles, while the curved surface of the cylinder is the rectangle.

The surface area = Area of the 2 circles + area of the rectangle

Take π as 3.14

radius of circle = ½ of 4 = 2 in

Area of the 2 circles = 2(πr²) = 2*3.14*2²

Area of the 2 circles = 25.12 in²

Area of the rectangle = L*W

width is given as 10 in.

Length (L) = the circumference or perimeter of the circle = πd = 3.14*4 = 12.56 in

Area of rectangle = L*W = 12.56*10 = 125.6 in²

Surface area of net = Area of the 2 circles + area of the rectangle

= 25.12 + 125.6 = 150.72 in²

4. Surface area of the net (S.A) = 2(area of triangle) + 3(area of rectangle)

=
`2(0.5*b*h) + 3(l*w)`

Where,

b = 8 cm

h =
`√(8^2 - 4^2) = √(48) = 6.9 cm} (Pythagorean theorem)</p><p>w = 8 cm</p><p>[tex]S.A = 2(0.5*8*6.9) + 3(20*8)`

`S.A = 2(27.6) + 3(160)`

`S.A = 55.2 + 480`

`S.A = 535.2 cm^2`