Constructing a Box, An open box is to be constructed from a square sheet of sheet metal with dimensions x feet by x feet by removing a square of side 1 feet from each corner and turning up the edges. The volume V of the box is V ( x ) = ( x − 2 ) 2 . Find the dimensions of the sheet metal needed to make a box that will hold 4 cubic feet by solving the equation V ( x ) = 4 .
Constructing a Box, An open box is to be constructed from a square sheet of sheet metal with dimensions x feet by x feet by removing a square of side 1 feet from each corner and turning up the edges. The volume V of the box is V ( x ) = ( x − 2 ) 2 . Find the dimensions of the sheet metal needed to make a box that will hold 4 cubic feet by solving the equation V ( x ) = 4 .
Solution Summary: The author explains how to calculate the dimensions of the sheet metal needed to make a box that will hold 4 cubic feet by solving the equation V(x)=4.
Constructing a Box, An open box is to be constructed from a square sheet of sheet metal with dimensions x feet by x feet by removing a square of side 1 feet from each corner and turning up the edges. The volume
V
of the box is
V
(
x
)
=
(
x
−
2
)
2
. Find the dimensions of the sheet metal needed to make a box that will hold 4 cubic feet by solving the equation
V
(
x
)
=
4
.
Find the volume of the solid bounded below by the circular cone z = 2.5√√√x² + y² and above by the
sphere x² + y²+z² = 6.5z.
Electric charge is distributed over the triangular region D shown below so that the charge density at (x, y)
is σ(x, y) = 4xy, measured in coulumbs per square meter (C/m²). Find the total charge on D. Round
your answer to four decimal places.
1
U
5
4
3
2
1
1
2
5
7
coulumbs
Let E be the region bounded cone z = √√/6 - (x² + y²) and the sphere z = x² + y² + z² . Provide an
answer accurate to at least 4 significant digits. Find the volume of E.
Triple Integral
Spherical Coordinates
Cutout of sphere is for visual purposes
0.8-
0.6
z
04
0.2-
0-
-0.4
-0.2
04
0
0.2
0.2
x
-0.2
04 -0.4
Note: The graph is an example. The scale and equation parameters may not be the same for your
particular problem. Round your answer to 4 decimal places.
Hint: Solve the cone equation for phi.
* Oops - try again.
Chapter 2 Solutions
Pearson eText for Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry -- Instant Access (Pearson+)
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