Answer:
1)556.11 cm²
2)164.05 cm²
3)117.70 cm²
Explanation:
1) We have a cylinder and a cone on top of it.
Formula for total surface area of cylinder is;
T.S.A = 2πrh + 2πr²
However, the top is not available for calculation here. Thus, we will use;
TSA = 2πrh + πr²
Thus;
TSA = 2π(5 × 12) + π(5)²
TSA = 455.53 cm²
The top is a cone but it's bottom is not included and so we will use lateral surface area of cone = πrL
L is the slanting height and can be calculated from pythagoras theorem ;
L = √(5² + 4²)
L = √41
Thus;
LSA = π × 5 × √41 = 100.58 cm²
Overall surface area = 455.53 + 100.58. Overall surface area = 556.11 cm²
2) for the box down;
TSA = 2lw + 2lh + 2hw
Since the top face is not used, then
TSA = lw + 2lh + 2hw
TSA = (5 × 5) + 2(5 × 5) + 2(5 × 5)
TSA = 125 cm²
For the prism on top, since the bottom is not included, we will use lateral surface are;. LSA = ½Pl
Where P is perimeter of base and L is slant height.
P = 5 × 4 = 20 cm
Radius is 5/2 = 2.5 and so using pythagoras theorem;
L = √(2.5² + 3²)
L = 3.905 cm
Thus;
LSA = ½ × 20 × 3.905 = 39.05 cm²
Overall surface area = 39.05 + 125 = 164.05 cm²
C) for the box down;
TSA = 2lw + 2lh + 2hw
Since the top face is not used, then
TSA = lw + 2lh + 2hw
TSA = (4 × 4) + 2(4 × 4) + 2(4 × 4)
TSA = 80 cm²
For the half cylinder on top;
Surface area ;
T.S.A = 2πrh + 2πr²
Since half cylinder;
TSA = πrh + πr²
TSA = π((2 × 4) + 2²))
TSA = 37.7 cm²
Overall total surface area = 80 + 37.7 ( 117.70 cm²