Question
In: Advanced Math
Let K be a cone with a circular bottom, that has a radius r, and the...
Let K be a cone with a circular bottom, that has a radius r, and the apex is directly above the center of the bottom. Let h represent the height of the cone. Show that the surface area of the cone K without the bottom is equal to
pi * r * sqrt(r^2 + h^2) .
(Use that a sector that is given with angle θ in a circle with radius R has the area (θ * R^2)/2
Solutions
Colby Messinger answered 2 years agoRelated Solutions
A transparent cylindrical tube with radius r = 1.50 cm has a flat circular bottom and...
A transparent cylindrical tube with radius r = 1.50 cm has a
flat circular bottom and a top that is convex as seen from above,
with radius of curvature of magnitude 2.60 cm. The cylinder is
filled with quinoline, a colorless highly refractive liquid with
index of refraction n = 1.627. Near the bottom of the tube,
immersed in the liquid, is a luminescent LED display mounted on a
platform whose height may be varied. The display is the letter...
A transparent cylindrical tube with radius r = 1.50 cm has a flat circular bottom and...
A transparent cylindrical tube with radius r = 1.50 cm has a
flat circular bottom and a top that is convex as seen from above,
with radius of curvature of magnitude 2.60 cm. The cylinder is
filled with quinoline, a colorless highly refractive liquid with
index of refraction n = 1.627. Near the bottom of the tube,
immersed in the liquid, is a luminescent LED display mounted on a
platform whose height may be varied. The display is the letter...
A transparent cylindrical tube with radius r = 1.50 cm has a flat circular bottom and...
A transparent cylindrical tube with radius r = 1.50 cm has a
flat circular bottom and a top that is convex as seen from above,
with radius of curvature of magnitude 2.60 cm. The cylinder is
filled with quinoline, a colorless highly refractive liquid with
index of refraction n = 1.627. Near the bottom of the tube,
immersed in the liquid, is a luminescent LED display mounted on a
platform whose height may be varied. The display is the letter...
The radius of a circular truncated cone varies with x as R(x) = (r/L)(8L-0.5x). Determine the...
The radius of a circular truncated cone varies with x as R(x) =
(r/L)(8L-0.5x). Determine the extension of the truncated con due to
it's own weight in terms of E, L, r,and Y. Where E and Y are the
modulus of elasticity and the specific weight of the material,
respectively.
The surface area of a right-circular cone of radius r and height h is S=πrr2+h2−−−−−−√, and...
The surface area of a right-circular cone of radius r and height
h is S=πrr2+h2−−−−−−√, and its volume is V=1/3πr2h.
(a) Determine h and r for the cone with given
surface area S=4 and maximal volume V.
h= , r=
(b) What is the ratio h/r for a cone with given
volume V=4 and minimal surface area S?
hr=
(c) Does a cone with given volume V and maximal
surface area exist?
A. yes
B. no
1.Consider a satellite of the earth in a circular orbit of radius R. Let M and...
1.Consider a satellite of the earth in a circular orbit of
radius R. Let M and m be the mass of the earth and that of the
satellite, respectively. Show that the centripetal acceleration of
the satellite is aR =
-(v^2/R)*(r/r) where v = |v| is
the magnitude of the velocity V and
r/r is a unit vector in the radial direction.
2.Using Newton's second low of motion and the law of universal
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An arrow lands uniformly random on a circular target of radius r. Let y and z...
An arrow lands uniformly random on a circular target of radius
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(a) Are Y and Z independent?
(b) Are Y and Z uncorrelated?
The tank in the form of a right-circular cone of radius 7 feet and height 39...
The tank in the form of a right-circular cone of radius 7 feet
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governing the height h of the leaking water is
dhdt=_______________
If the tank is initially full, it will take _________ seconds to
empty.
A metallic circular plate with radius r is fixed to a tabletop. An identical circular plate...
A metallic circular plate with radius r is fixed to a tabletop.
An identical circular plate supported from above by a cable is
fixed in place a distance dd above the first plate. Assume that dd
is much smaller than r. The two plates are attached by wires to a
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1) What is the tension in the cable? Neglect the weight of the
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Express your answer in terms of the variables d, r, V,...
A cone has radius 4 and slant height 5. The cone is melted down and recast...
A cone has radius 4 and slant height 5. The cone is melted down
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