Question

A right square pyramid has a height of 50 meters (from the center of the base to the apex) and a base with sides 50 meters long. (a) Determine the volume of the pyramid. (b) Determine the surface area of the pyramid, not including the base.

(a) Determine the volume of the pyramid.

(b) Determine the surface area of the pyramid, not including the base.

Answer #1

A pyramid has a height of 461 ft and its base covers an area of
11.0 acres (see figure below). The volume of a pyramid is given by
the expression
V =
1
3
Bh,
where Bis the area of the base and h is the
height. Find the volume of this pyramid in cubic meters. (1 acre =
43,560 ft2)

Find the center of mass of a square base pyramid where the side
length of the base is 20 m, the height is 9 m, and the pyramid has
constant mass density δ kg/m3.

A heat conductor has a shape of a pyramid. The base is square
shaped, with sides 4 mm long, each. The
height of the pyramid is 12 mm. The pyramid has been placed on a
heating element with constant
temperature 300°C. Heat is directed through the top of the pyramid
so that the temperature at the height
of 10 mm is 100 °C. Assuming the heating power and heat
conductivity of the material remaining constant,
compute the temperature of the...

A box with an open top has a square base and four sides of equal
height. The volume of the box is 225 ft cubed. The height is 4 ft
greater than both the length and the width. If the surface area is
205 ft squared. what are the dimensions of the box?
What is the width of the box?.
What is the length of the box?

Find the work it would take to build a limestone pyramid with a
square base with sides 560 ft and a height of 400 feet. (the
density of limestone is 150 lb/ft3

A rectangular box must have a volume of 2 cubic meters. The
material for the base and top costs $ 2 per square meter. The
material for the vertical sides costs $ 8 per square meter. (a)
Express the total cost of the box in terms of the length (l) and
width (w) of the base. C = $ (b) Find the dimensions of the box
that costs least. length = meters width = meters height =
meters

A circular cone is 10 cm wide at the base and has a slant height
of 8.5 cm. Determine:
a. Volume of the cone =
b. Total surface area of the cone =
c. The angle the slant height makes with the base diameter =
d. The cylinder shown here has the same height and base radius
as the cone, by what percent the volume of
the cylinder exceeds the volume of the cone?

1. A six-sided box has a square base and a surface area of 54
m^2. Let V denote the volume of the box, and let x denote the
length of one of the sides of the base. Find a formula for V in
terms of x.
2. What is the maximum possible volume of the box in Problem 1?
Note that 0< x≤3√3.

A rectangular box with a square base has a volume of 4 cubic
feet. If x is the side length of the square base, and y is the
height of the box, find the total cost of the box as a function of
one variable The material for the bottom of the box costs $3 per
square foot, the top costs $2 per square foot, and the four sides
cost $5 per square foot. If x is the side length...

A box with a square base and open top must have a volume of
108000 cm^3. We wish to find the dimensions of the box that
minimize the amount of material used.
First, find a formula for the surface area of the box in terms of
only x, the length of one side of the square base.
[Hint: use the volume formula to express the height of the box in
terms of x.]
Simplify your formula as much as possible....

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