# Question: calculus problem af thanks in advance for whoever can help...

###### Question details

**Calculus Problem (a-f)** Thanks in advance for
whoever can Help!

1. Find the volume of the solid generated by revolving about

the x-axis the region in the first quadrant bounded by the

parabola **y = 6 –
x ^{2}** and the lines

**y = 0**and

**x = 0**.

a. Use two different methods to find points of intersection of

relevant curves.

b. Find arc length of all relevant curves.

c. Sketch and identify all bounded areas. Sketch relevant

elements and pre-draw all graphs.

d. Estimate all answers via High School methods and verify all

answers with calculus.

e. Find the volume using the shell/cylindrical shell method.

Use the appropriate
notation where **V _{cx}**,

**V**,

_{cy}**V**, and

_{cx}= 5
**V _{cy} = 2** denote the cylindrical shell
method is used and the

area is revolved about the x-axis and about the y-axis, and

the lines **x =
5** and **y = 2** respectively.

f. Use two different methods to find the surface areas of all

bounded areas.