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Asked by Thimma Last Modified
Answer Problem Solving: Finding Height and Total Surface Area of a Cylinder
Given Information:
Step 1: Finding the Height of the Cylinder
The formula for the volume of a cylinder is given by: V=πr2hV=πr2h
Where:
Substituting the given values: 2002=π×(7)2×h2002=π×(7)2×h
2002=49π×h2002=49π×h
h=200249πh=49π2002
Now, calculate the value of hh:
h≈200249×3.14h≈49×3.142002
h≈2002153.86h≈153.862002
h≈12.99 cmh≈12.99cm
So, the height of the cylinder is approximately 12.99 cm12.99cm.
Step 2: Finding the Total Surface Area of the Cylinder
The formula for the total surface area of a cylinder is given by: A=2πrh+2πr2A=2πrh+2πr2
Where:
Substituting the given values: A=2π×7×12.99+2π×(7)2A=2π×7×12.99+2π×(7)2
A=2π×7×12.99+2π×49A=2π×7×12.99+2π×49
A=2π×90.93+98πA=2π×90.93+98π
A=181.86π+98πA=181.86π+98π
A=279.86πA=279.86π
Now, calculate the value of AA:
A≈279.86×3.14A≈279.86×3.14
A≈878.66 cm2A≈878.66cm2
So, the total surface area of the cylinder is approximately 878.66 cm2878.66cm2.
Conclusion:
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