Please help me with the following questions.

1.

Find the volume of the largest right circular cone that can be inscribed in a sphere of radius 13 13 13 V =1 cubic units (Round to two decimal places as needed.)What are the dimensions of the lightest open-top right circular cylindrical can that will hold a volume of 1728 cm3? The radius of the can is cm and its height is cm (Type exact answers, using x as needed.)Determine the dimensions of the rectangle of largest area that can be inscribed in the right triangle shown in the accompanying figure 113 W 112 h The width of the rectangle with largest area is |units The height of the rectangle with largest area is unitsA silo (base not included) is to be constructed in the form of a cylinder surmounted by a hemisphere. The cost of construction per square unit of surface area is 4 times as great for the hemisphere as it is for the cylindrical sidewall. Determine the dimensions to be used if the volume is fixed at 2000 cubic units and the cost of construction is to be kept to a minimum. Neglect the thickness of the silo and waste in construction. The radius of the cylindrical base (and of the hemisphere) is |ft. (Round to the nearest tenth as needed.)ds Given the velocity v = dt and the initial position of a body moving along a coordinate line, find the body's position at time t. v= 9.8t + 2, s(0) = 14 s(1) =A silo (base not included) is to be constructed in the form of a cylinder surmounted by a hemisphere. The cost of construction per square unit of surface area is 2 times as great for the hemisphere as it is for the cylindrical sidewall Determine the dimensions to be used if the volume is fixed at 14000 cubic units and the cost of construction is to be kept to a minimum. Neglect the thickness of the silo and waste in construction The radius of the cylindrical base (and of the hemisphere) is it. (Round to the nearest tenth as needed.)