Answer:
3. 150.72 in²
4. 535.2cm²
Step-by-step 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)
= [tex] 2(0.5*b*h) + 3(l*w) [/tex]
Where,
b = 8 cm
h = [tex] \sqrt{8^2 - 4^2} = \sqrt{48} = 6.9 cm} (Pythagorean theorem)
w = 8 cm
[tex]S.A = 2(0.5*8*6.9) + 3(20*8)[/tex]
[tex]S.A = 2(27.6) + 3(160)[/tex]
[tex]S.A = 55.2 + 480[/tex]
[tex]S.A = 535.2 cm^2[/tex]
