A metal solid made up of a cylindrical bar fixed onto a cube. The cylindrical bar fixed onto a cube. The cylindrical bar is 20 cm long and has a diameter of 7 cm. Each side of the cube is 9 cm long.
The surface of the solid was painted. What area in area in cm2 was painted? (Take π
=22/7 )
area of cube = 6*49
subtract pi (3.5^2)
so cube area painted = 294 - pi(3.5)^2
side area of cylinder = 20 ( 7 pi)
end areas = 2 pi(3.5^2) but delete one
so total cylinder area =140 pi+pi(3.5^2)
total = 294-pi(3.5)^2+140pi+pi(3.5)^2
= 294 + 140 pi
= 294 + 20(22) = 294+440 = 734
area of cube = 6*81
= 486
oh 486 + 440
Open cylinder
Pi3.5^2 =38.5
2pi3.5^2×20= 440
440+38.5= 478.5
Cube
6l^2 = 6×81 = 486
486-38.5 =447.5
447.5 + 486= 926
To determine the area that was painted on the metal solid, we need to calculate the surface area of both the cylindrical bar and the cube, and then add them together.
1. Surface area of the cylindrical bar:
The surface area of a cylinder can be calculated using the formula:
A_cylinder = 2πrh + 2πr^2
In this case, the height (h) of the cylindrical bar is given as 20 cm, and the radius (r) can be calculated by dividing the diameter (7 cm) by 2.
So, the radius (r) = 7 cm / 2 = 3.5 cm.
Now, substitute the values into the formula to find the surface area of the cylindrical bar:
A_cylinder = 2 * (22/7) * 3.5 * 20 + 2 * (22/7) * 3.5^2
Simplify the equation:
A_cylinder = 44 * 3.5 * 20 + 22 * 3.5^2
A_cylinder = 3080 + 269.5
A_cylinder ≈ 3349.5 cm^2
2. Surface area of the cube:
The surface area of a cube can be calculated by multiplying the length of one side by itself, and then multiplying the result by 6 (since a cube has 6 faces).
In this case, each side of the cube is given as 9 cm.
So, the surface area of the cube = 6 * 9 * 9 = 486 cm^2.
3. Total area painted:
To find the total area painted, we need to add the surface area of the cylindrical bar and the surface area of the cube.
Total area painted = A_cylinder + Surface area of the cube
Total area painted ≈ 3349.5 cm^2 + 486 cm^2
Total area painted ≈ 3835.5 cm^2
Therefore, the area painted on the metal solid is approximately 3835.5 cm^2.