Recall that the volume of a sphere or radius r is V = Find the rate of change of the volume of a sphere with respect to the radius, r. Then find the rate when r = 12 dV a) O dr 4r r; Rate = 2887 %3D dV = 4rn; Rate = 5767 dr b) O AP %3D 2rn; Rate = 2887 c) dr AP = 4rn; Rate = 487 d) O dr dV 2ra; Rate 247

Q: At what angle in degrees must the cutting plane through the center of the base of the cylinder with…

A: The general formula for the cylinder in a 3D coordinate system is . Here, a is the radius of the…

Q: 1. Show that the volume ofa parallelepiped with sides A. B and C given by A (B x C)

A: As per our guidelines we are supposed to solve only one question i.e. the question no 1. For the…

Q: A machinist is required to manufacture a circular metaldisk with area 100 cm2 .(a) What radius…

A: Let the radius = r cm  So the area is =πr2 cm2 .

Q: A closed cylindrical tank of circular cross-section has a radius of 2 ft. and a height of 6 ft. Use…

A: Radius = 2 ft Height = 6 ft dr = 1 inchdr =112 ftdh = 1 + 1 (top+bottom)dh = 2 inchdh = 212 ft

Q: Find the volume of a hemispherical shell having outer radius a and inner radius b if the density…

A: Mass density is defined as the mass per unit volume. gm/cm3 is, therefore, a unit of mass density.…

Q: The radius of a sphere was measured and found to be 3 ft with a maximum error of 0.1 inches. Find…

A: Given r=3ft=36inches  dr=0.1

Q: A tumor is approximately spherical. If the radius of the tumor changes from 14 mm to 16 mm, find the…

A: A sphere has radius 14mm and 16mm

Q: A planer takes a 1/16 in. Cut on a plate that is 3 1/2 in. Thick. What is the thickness of the plate…

A:

Q: The surface area of a sphere increases at a rate of 64 m2/sec. Then the rate at which the radius…

A: Given rate of increase in the surface of sphere=64m2/sec And radius of sphere=3m Now we have to find…

Q: A cone has a volume V. What base radius and height will minimize the lateral surface area?

A: Given, a cone with volume V. Let the slant height of the cone m , radius R and height H.   The…

Q: Find the volume of the smaller wedge cut from a sphere of radius 10 by two planes that intersect…

A: Here we have to find the volume of the similar wedge cut from a sphere of radius 10 by two planes…

Q: Prove that the area of a trapezoid whose altitude has length h and whose median has length m is A =…

A: Let's consider a trapezoid ABCD with bases AD=b1   and  BC=b2 and altitudes AE and DF measures h…

Q: Given a right circular cone of radius 5 cm and altitude is 10 cm, find the following: Lateral area…

A: Given  radius of right circular cone = 5cm  altitude =10cm

Q: Two identical spheres are placed so that one is on top of the other inside a right circular cylinder…

A: This question is related to cylinders and spheres, we will solve it using given information.

Q: For a right circular cylinder of height 25 ft, the radius was measured as 20 ft with an error of…

A: the volume of the right cylinder is given by the formula, V=πr2h where r is the radius of the…

Q: Si RW bisecta LSRU y RS RU, demuestre que 4TRU AVRS

A: Concept: Triangle congruence: If the three corresponding sides and the three corresponding angles…

Q: 5. Find the volume common to two circular cylinders, each of radius r, that intersect at right…

A:

Q: What is the pressure on a horizontal surface with an area of 2 m2 that is 4 m underwater?

A: The area of horizontal surface is A=2 m2 And the height is h=4 m

Q: The surface area of a sphere increases at a rate of 66 m2/sec. Then the rate at which the radius…

A:

Q: The radius of a sphere is 3 ft with a maximum error of 0.1 in. Find the approximate error in the…

A: V=(4pi*r^3)/3

Q: The measure of the linear density at any point of a rod 6 m long varies directly as the distance…

A: Given length of the rod=6 m Linear density at a distance 4 m from one end=3 kg/m We have to find the…

Q: Given that the altitude is 2/3 of the total altitude of a cone which is 10m and the base of the cone…

A: The volume of the frustum can be obtained using the formula V=13πH(R2+Rr+r2). Here, H is the height…

Q: The surface area of a sphere increases at a rate of 59 m?/sec. Then the rate at which the radius…

A: We have to find rate of change of radius

Q: A metal chain ladder, 20 meters long, has a linear density of 3 Newtons per meter, and hangs down…

A:

Q: A flexible tube of length 4 m is bent into an L-shape. Where shouldthe bend be made to minimize the…

A: A flexible tube of length 4m is bent into an L-shape. Let x,y be the length of sides of L-shape.…

Q: · A vertical gate, composed of a squa- re and a triangle, is submerged so that its upper edge…

A:

Q: A cylindrical storage tank has a depth of 5 ft and a radius measuring 2 ft. If ecach cubic foot can…

A: Given- A cylindrical stroage tank has a depth of 5 ft and radius m,easuring 2 ft. To find- The total…

Q: The surface area of a sphere increases at a rate of 90 m2/sec. Then the rate at which the radius…

A:

Q: The paper cup is  9 cm tall and the circular opening has a radius of 2.5 cm. What is the minimum…

A:

Q: For a right circular cylinder, suppose that r = 6 in and H = 7 in. Find the exact:  a) lateral area…

A: Given: For a right circular cylinder: Formula used:

Q: A cone and a cylinder each have radius of 3 and height 4 - ratio of 3:4. what is the ratio of their…

A: given,       A cone whose radius=3 and height =4A cylinder whose radius=3 and height =4

Q: Derive the formula for the volume of a sphere of radius r.

A: The volume of cylindrical element with radius x and altitude dy.                    dV  =  πx2 dy…

Q: According to Cavalieri's Principle, which pair of shapes would have equal volumes?

A: the volume of the cone, pyramid , cylinder , sphere , rectangular prism , are given by  volume of…

Q: The volume of a right circular cone is 36π. If its altitude is 2, find its radius?

A: From the given ques  the volume of the right circular cone (v) = 36π and the altiitude (h) = 2 R = ?…

Q: A can of tennis balls is twelve inches high and has a diameter of four inches. The can holds three…

A: Volume left between can and tenis balls =  Volume of cylinder - volume of 3 balls.

Q: The surface area of a sphere increases at a rate of 84 m2/sec. Then the rate at which the radius…

A:

Q: Find volume by evaluating vating triple integralspherical cordinates) use dp dodo Sin o

A:

Q: The surface area of a sphere increases at a rate of 57 m2/sec. Then the rate at which the radius…

A: Let r is the radius of the sphere . S is the surface area of the sphere. we know that…

Q: The volumes of two similar rectangular solids are 1000 cm3 and 64 cm3. What is the ratio of their…

A:

Q: A cylindrical tank is designed to have a radius of 5 m and a height of 7 , but that the radius and…

A:

Q: A wooden solid is made up of a cylinder with hemispherical ends. If the whole length of the solid is…

A: Radius of the cylinder, r = 7 cm Height of the Cylinder, h = (84 - 2r) cm…

Q: The flow rate of water via a 50mm dia. pipe is shown in the table below, into a storage tank with a…

A:

Q: Two identical spheres are placed so that one is on top of the other inside a right circular cylinder…

A: topic - volume of cylinder

Q: Find the mass of a straight circular rod of length a and radius b whose density varies as the square…

A:

Q: The height of a right circular cylinder is 1.5 times the radius of the base. What is the ratio of…

A: We know that the for a cylinder with radius r and height h, Total surface area is 2πrr+h. Lateral…

Q: The surface area of a sphere increases at a rate of 95 m2/ sec. Then the rate at which the radius…

A:

Q: The surface area of a sphere increases at a rate of 52 m2/sec. Then the rate at which the radius…

A: Let A is the surface area of Sphere.

Q: The surface area of a sphere increases at a rate of 82 m² / sec. Then the rate at which the radius…

A: Use rate of change

Q: An aluminum can is to be constructed to contain 2500 cm^3 of liquid. Let r and h be the radius of…

A:

Q: . A cone with radius 9 and slant height 15 has volume ___and lateral area____?

A: to find the volume and lateral area.

Cylinders

A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.

Cones

A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.