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 and recast as a cylinder with height 4. The radius of the cylinder is? Show your work.

Expert Solution

milcah answered 2 years ago

A solid sphere has a temperature of 674 K. The sphere is melted down and recast...

A solid sphere has a temperature of 674 K. The sphere is melted down and recast into a cube that has the same emissivity and emits the same radiant power as the sphere. What is the cube's temperature in kelvins?

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 and height 39 feet standing on its end, vertex down, is leaking through a circular hole of radius 4 inches. Assume the friction coefficient to be c=0.6 and g=32ft/s^2 . Then the equation governing the height h of the leaking water is dhdt=_______________ If the tank is initially full, it will take _________ seconds to empty.

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

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

Optimization of a cylinder container with a height of 4 inches and a radius of 1.25...

Optimization of a cylinder container with a height of 4 inches and a radius of 1.25 inches in terms of either volume OR surface area. Please provide: (A) Calculation of surface area/volume of the container. (B) Primary and secondary constraint equations (C) Derivative of primary equation (D) Optimized dimensions and how they were determined (number-line analysis to show that the dimensions result in an optimized solution. (E) Graph of optimization (in terms of volume OR surface area in terms of...

A conical tank has height 9 m and radius 4 m at the base. Water flows...

A conical tank has height 9 m and radius 4 m at the base. Water flows at a rate of 3 m^3/min. How fast is the water level rising when the level is 1 m and 2 m? (Use symbolic notation and fractions where needed.) When the water level is 1 m, the water level is rising at a rate of _ .When the water level is 2 m, the water level is rising at a rate of _.

A ball rolls down from the top of an incline with a height of 5 m...

A ball rolls down from the top of an incline with a height of 5 m high without slipping. The ball has a diameter of 0.2m. What are the ball’s translational speeds a) at the center of the ball, b) at the contact point on the ground, and c) at the top of the ball when it arrives at the bottom? What values of "c" do you expect for hollow/solid balls? Will the hollow ball be faster?

A cylindrical soda can has a radius of 6cm and a height of 12cm. When the...

A cylindrical soda can has a radius of 6cm and a height of 12cm. When the can is full of soda, the center of mass of the contents of the can is 6cm above the base on the axis of the can (halfway along the axis of the can). As the can is drained, the center of mass descends for a while. However, when the can is empty (filled only with air), the center of mass is once again 6cm...

A solid cylinder (radius = 0.150 m, height = 0.120 m) has a mass of 7.36...

A solid cylinder (radius = 0.150 m, height = 0.120 m) has a mass of 7.36 kg. This cylinder is floating in water. Then oil (ρ = 851 kg/m3) is poured on top of the water until the situation shown in the drawing results. How much of the height of the cylinder is in the oil?

A solid cylinder (radius = 0.190 m, height = 0.190 m) has a mass of 21.4...

A solid cylinder (radius = 0.190 m, height = 0.190 m) has a mass of 21.4 kg. This cylinder is floating in water. Then oil (ρ = 867 kg/m3) is poured on top of the water until the situation shown in the drawing results. How much of the height of the cylinder is in the oil?

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