Question

Determine the height in meters of a perfect cube with a volume of
eight million cubic feet using 1 ft = 0.3048 m, and then determine
the area in square meters of a circle with a diameter of 80
cm.

Answer #1

A cylindrical can is to have volume 1500 cubic centimeters.
Determine the radius and the height which will minimize the amount
of material to be used.
Note that the surface area of a closed cylinder is
S=2πrh+2πr2 and the volume of a cylindrical can is
V=πr2h
radius =. cm
height = cm

Darcy's law gives us the volume flow rate-volume per
time (for example, cubic meters per day, m^3/day). Another way to
express volume is on a per-unit-area basis. For example,
if we have a 1-m^3 cube, we know its base is 1 m^2 the
cross-sectional area of the cube-and its height is 1m. If we fill
the cube with water, we can say we have 1m of water per unit area.
Darcy's law can be rearranged to calculate the volume flow...

6. The volume of a cube is increasing at a rate of 10 cubic
cm/min. How fast is the surface area of the cube increasing when
the length of the edge is 30 cm?

3. For a sample of 15trees, the volume of lumber (y) (in cubic
meters) and the diameter (x) (in centimeters) at a fixed height
above ground level was measured. The following summary statistics
were obtained:(10points)x̄= 35.2sx= 8.9ȳ= 0.78sy= 0.48r=
0.95a)Compute the least-squares regression line for predicting
volume from diameter.b)Predict the volumefor a tree whose diameter
is 42centimeters.

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 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.

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)

1. The following measurements are taken of a box.
length = 84 cm
height = 40 cm
width = 30 cm
Calculate the volume of the block in cubic meters.
2. In a reaction time experiment, three displacements were
recorded: 40 cm, 50 cm, and 47 cm. Calculate the average
displacement (in m).
3. 5.9 square meter equals how many square centimeters?

Gravel is being dumped from a conveyor belt at a rate of 10
cubic feet per minute. It forms a pile in the shape of a right
circular cone whose base diameter and height are always equal. How
fast is the height of the pile increasing when the pile is 13 feet
high. Recall that the volume of a right circular cone with the
height h and radius of the base r is given by
V=1/3pi r*2h
Answer in ft/min

1.) A rock is thrown into a still pond. The circular ripples move
outward from the point of impact of the rock so that the radius of
the circle formed by a ripple increases at a rate of 5
ft./min.
Find the rate at which the area is changing at the instant the
radius is 7 feet.
when the radius is 7 feet, the area is changing at approximately __
Square feet per minute
2.)
The radius of a spherical...

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