can some one please help me im confused The radius of a cylinder is 3.5 ft. The height is 14 ft. Find the surface area and volume of the cylinder to the nearest tenth of a foot. Show your work. what is the answer
The formula for the surface area of a cylinder is T.S.A.= 2πrh+2πr^2 where 2πrh represents the lateral area while 2πr^2 represents the combined area of the bases. Since we know r=3.5ft and h=14ft, then we have:
T.S.A.= 2πrh+2πr^2
T.S.A.= 2π(3.5)(14)+2π(3.5)^2
T.S.A.= 2π(49)+2π(12.25)
T.S.A.= 98π+24.5π
T.S.A.= 122.5π
T.S.A.= 384.8451 ft^2
The formula for the volume of a cylinder is V = π*r^2*h
Since we know that r=3.5ft and h=14ft, then the volume of the cylinder is:
V = π*r^2*h
V = π*3.5^2*14
V = π*12.25*14
V = π*171.5
V = 171.5π
V = 538.783 ft^3
Hope this was helpful! Let me know if you would like me to clarify anything!
To find the surface area and volume of the cylinder, you can use the following formulas:
Surface Area of a Cylinder: SA = 2πr(r + h)
Volume of a Cylinder: V = πr^2h
First, let's calculate the surface area:
Given: Radius (r) = 3.5 ft and Height (h) = 14 ft
Step 1: Calculate the surface area (SA)
SA = 2πr(r + h)
Plug in the values:
SA = 2π(3.5)(3.5 + 14)
Step 2: Simplify the expression:
SA = 2π(3.5)(17.5)
Step 3: Evaluate the multiplication:
SA = 2(3.14)(3.5)(17.5)
Step 4: Calculate the final result using a calculator:
SA ≈ 384.84 ft² (rounded to the nearest tenth)
Therefore, the surface area of the cylinder is approximately 384.8 ft².
Now, let's calculate the volume:
Given: Radius (r) = 3.5 ft and Height (h) = 14 ft
Step 1: Calculate the volume (V)
V = πr^2h
Plug in the values:
V = π(3.5)^2(14)
Step 2: Simplify the expression:
V = π(12.25)(14)
Step 3: Evaluate the multiplication:
V = 3.14(12.25)(14)
Step 4: Calculate the final result using a calculator:
V ≈ 618.47 ft³ (rounded to the nearest tenth)
Therefore, the volume of the cylinder is approximately 618.5 ft³.
In summary:
- The surface area of the cylinder is approximately 384.8 ft².
- The volume of the cylinder is approximately 618.5 ft³.
From Google:
A cylinder's volume is π r² h, and its surface area is 2π r h + 2π r².