Surface Area of Cylinders

Question

A cardboard shipping container is in the form of a cylinder with a radius of 6 centimeters and a volume of 8595.4 cubic centimeters.

 

What is the length of the shipping container?

 

What is the surface area of the shipping container?

Answer 1

Hi, Conny!

 

The volume for a cylinder is founding using area of the base x the height (V = Bh). The base is the circle with radius 6 cm, the "height" of the cylinder is the length of the shipping container. Area of the base is pi x radius squared (A = πr²). 

 

V = πr² ⋅ h

 

Substituting what we know into the formula gives us:

 

8595.4 cm³ = pi ⋅ (6 cm)² ⋅ h cm

 

8595.4 = pi ⋅ 36 ⋅ h               Divide both sides by 36pi

 

76.00 = h                             (I used 3.14159 for pi)

 

The length of the container is 76 cm.

 

The surface area of a cylinder is found using the lateral surface area (area of the sides) plus the area of the two bases (SA = 2pi⋅rh + 2pi⋅r²). The lateral surface area is found using the circumference of the base times the height. We already know the area of a base. 

 

SA = (2⋅pi⋅6⋅76) + (2⋅pi⋅36)

 

     = (2,865.130) + (226.194)

 

     = 3,091.325 cm²

 

Hope this helps!

Kathye P.

Answer 2

a) Volume = (Area of the base)x(Length) = (pi)r²L

 

8595.4 = (3.14159)(6²)(L)

 

Solve for L, the length of the cylinder

 

b) The surface area is:

 

Surface Area = (Area of top and bottom circles)+(Area of the length of the cylinder)

 

The area of each circle is (pi)r².  Since there are two of them (top and bottom), the total area is 2(pi)r² =2(3.14159)(6²)

 

The area along the length is a rolled up rectangle of length L that we just solved for in part a.  The width is the circumference of the top/bottom circles = 2(pi)r.

 

Surface Area = (2)(3.14159)(6²) + (L)(2)(3.14159)(6)

 

Where L is the cylinder's length from part a above