QUESTION 2 c) A glass cone has a circular base with a radius of 30+0.25mm. The...
Please help this one A right-circular cone with base radius r, height h, and volume ar," is positioned so that the base sits in the x-y plane with its center at the origin. The cone points upwards in the +z-direction. Starting from the definition, find and expression for the z-coordinate of the center of mass of a homogeneous right-circular cone. Verify the units and the magnitude of your answer to part (a) Briefly explain how you could experimentally verify your...
please answer 1,2&3! A right circular cone has a radius of 4z +4 and a height of 3 units less. Express the volume of the cone as a polynomial function. The volume of a cone is V = ?h for a radius r and height h. Preview V(z) = A square has sides 13 units. Squares of z +2 by +2 units are cut out of each corner to create an open box. Express the volume of the box as...
4. Use the AM-GM inequality to find the largest right circular cylinder that is inscribed in a right cone with base radius R and height H. Also determine the radius and height of the largest such cylinder. 4. Use the AM-GM inequality to find the largest right circular cylinder that is inscribed in a right cone with base radius R and height H. Also determine the radius and height of the largest such cylinder.
Problem 3 A water tank has the shape of an inverted circular cone with base radius Rand height H. If water is being pumped into the tank, and at certain timeo 0, (in seconds) the height of the water is given by h(t). (a) Sketch h(t) for t0. (Briefly, sketch the diagram, however, indicate the maximum height on the y axis.) (b) Is the graph concave upward or concave downward? e Suppose a bce Which do you think r he)-Ex...
A solid right circular cone has radius 2 and height 4. Suppose the density of the cone above has a density that varies as the square of the distance from the base. Find the center of mass.
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.
The radius and height of a right circular cone are measured with errors of 2% and 3% respectively. Use differentials to approximate the maximum percentage error in the 1. calculated yolume. The radius and height of a right circular cone are measured with errors of 2% and 3% respectively. Use differentials to approximate the maximum percentage error in the 1. calculated yolume.
The volume of a cone is given by V = TP /s. How fast is the radius of the base where the radius of the baser and height h are both functions of time. Suppose when r= 4 m, h=8 m and the height is decreasing by 8 m/s, you are told that the volume is increasing by 87 m changing? (Round your answer to 3 decimal places). Submit Answer Tries 0/3
36 SSM The volume of a cone of height h and base radius r is V-Tr2h/3. A conical vessel of height 25 cm rest- ing on its base of radius 15 cm is filled with water. (a) Find the volume and weight of the water in the vessel. (b) Find the force exerted by the water on the base of the vessel. Explain how this force can be greater than the weight of the water.
1. Consider a solid cone with uniform density p, height h, and circular base with radius R (hence mass M,sphR2). Let the vertex of the cone be the origin ofthe body frame. By symmetry, choose basis vectors e for the body frame such that the inertia tensor I, is diagonal. Will this rigid body with this body origin be an asymmetric top, a symmetric top, or a spherical top? Calculate the inertia tensor in this basis How will the inertia...