Answer:
The radius is increasing at a rate of 62832 cubic millimeters per second when the diameter is of 100 mm.
Step-by-step explanation:
Volume of a sphere:
The volume of a sphere of radius r is given by:
How fast is the volume increasing:
To find this, we have to differentiate the variables of the problem, which are V and r, implicitly in function of time. So
The radius of a sphere is increasing at a rate of 2 mm/s.
This means that
How fast is the volume increasing (in mm3/s) when the diameter is 100 mm?
Radius is half the diameter, so
Then
The radius is increasing at a rate of 62832 cubic millimeters per second when the diameter is of 100 mm.
Answer:
Step-by-step explanation:
A rectangular prism (or orthohedron) is a polyhedron whose surface is formed by two equal and parallel rectangles called bases and by four lateral faces that are also parallel rectangles and equal two to two.
The orthohedron is a straight prism and also a particular case of irregular quadrangular prism.
In a rectangular prism you can differentiate the following elements:
Bases: are two parallel and equal rectangles.
Faces: the four rectangles of the lateral faces and the two bases. Therefore, it has six faces.
Height : distance between the two bases of the prism. The height h coincides with any of the edges of the lateral faces.
Vertices: the eight points where three faces of the prism converge.
Edges: segments where two faces of the prism are found.
The surface area of the rectangular prism (or orthohedron) is calculated by the following formula:
where w is width, l is length, and h is height.
Solving with l = 15mm, w = 3mm, and h = 4mm
9514 1404 393
Answer:
(b) 1
Step-by-step explanation:
Three points not on the same line uniquely define one plane.
Just use the equations x + y= 47 and 2x + 4y=138 to solve
The answer is choice A- 68