Answer:
2243.7 cm^2 to the nearest tenth.
Step-by-step explanation:
Total volume = volume of cylinder + volume of the cone
= πr^2h + 1/3πr^2(59 - h) where h is the height of the cylinder.
So 6622 = π(7)^2h + 1/3π(7)^2(59 - h)
49πh + 49/3 π * 59 - 49/3 π h = 6622
49πh - 49/3 π h = 6622 - 49/3 π * 59
h( 49π - 49/3 π) = 6622 - 49/3 π * 59
h = (6622 - 49/3 π * 59) / ( 49π - 49/3 π)
h = 35.026 cm = height of the cylinder.
So the height of the cone = 59 - 35.026 = 23.974.
Next we find the slant height of the cone (L).
L^2 = 7^2 + 23.974^2
= 623.753
L = 24.975
The surface area of the whole solid
= surface area of the exposed cylinder + lateral surface area of the cone
= πr^2 + 2π*h + πrL
= π(7)^2 + 14π*35.026 + π(7)*24.975
= 2243.69 cm^2.
