Luther is building a model rocket for a science fair project. He attaches a nose cone to a cylindrical body to
form the rocket's fuselage. The rocket has a diameter of 4 inches and a total height (including the nosecone)
of 19 inches. The nosccone is 7 inches tall. What is the surface area of the rocket?

209.105 in2

Step-by-step explanation:

First we can find the surface area of the cylindrical part, which include the bottom base and the side area, so we have:

S1 = pi*r^2 + 2*pi*r*h

Where S is the surface area, r is the radius and h is the height.

The rocket has a height of 19 inches, and the cone has 7 inches of height, so the cylinder has 19 - 7 = 12 inches of height. The radius is half the diameter, so the radius is 2 inches. Then, we have:

S1 = pi*2^2 + 2*pi*2*12 = 163.3628 in2

For the cone, the surface area (without the base) is given by:

S2 = pi * r * s

where s is the slant height, given by:

s^2 = h^2 + r^2

s^2 = 7^2 + 2^2 = 53

s = 7.2801 in

So we have that:

S2 = pi * 2 * 7.2801

S2 = 45.7422 in2

Summing S1 and S2, we have:

S = S1 + S2 = 163.3628 + 45.7422 = 209.105 in2

the volume is the product of the area of the base, 3x(3x+4), and the height, 3x-1

step-by-step explanation: