The radius of a sphere increases at the rate of 4 m/sec. Find the rate at which the volume of a sphere increases when the radius is 19 m.

Q: Coffee is draining out of a conical filter at a rate of 2.25 in3>min. If the cone is 5 in tall…

A: Given: The change in volume for the filter is -2.25 in3/min The change in volume for the coffee pot…

Q: If a snowball melts so that its surface area decreases at a rate of 1cm /min, find the rate at which…

A: Diameter= DRadius = r =D/2Surface area = A= 4pi*r^2Given dA/dt= -1 cm^2/min (negative because…

Q: 1. The side of a cube increases at the rate of 23 m/sec. Find the rate at which the volume of the…

A:

Q: . Find the rate at which the volume increases when the radius is 30 cm. (Hint: Volume 4 of the…

A:

Q: A spherical balloon is inflated with air at a rate of 32 cm3/ min. At what rate does the radius…

A: Find dr/dr.

Q: The volume of a cube decreases at a rate.1 of 15 m/sec. Find the rate at which the side of the cube…

A: It is given that the volume of a cube is decreasing at a rate of 15 m/sec. It is known that volume…

Q: The surface area of a sphere increases at a rate of 87 m/sec. Then the rate at which the radius…

A:

Q: If a ball of candy is covered in chocolate and is melting so that its surface area decreases at a…

A: To find: The rate at which diameter decreases when diameter is 10 cm. Given: The rate of surface…

Q: A cube’s surface area increases at the rate of 72 in2/sec. At what rate is the cube’s volume…

A: Given:

Q: The volume of the sphere is increasing at the rate of 6cm^3/hr. At what rate is its surface area…

A: Given that the volume of the sphere is increasing at the rate of 6  cm^3/hr. We have to find the…

Q: If the rate of change of the surface area of a sphere with respect to its radius is 16pi sq cm, find…

A:

Q: Water is running out of a conical funnel at the rate of 1000 cu mm/sec. If the radius of the funnel…

A: The volume of a cone is one-third of the volume of a cylinder, so the formula for the cone is given…

Q: The side of a cube is increasing at a rate 7m/s, then the rate at which the volume of the cube…

A: Let s be the side of the cube in meter and V be the volume of the cube and t be the time in…

Q: If a snowball melts so that its surface area decreases at a rate of 2 cm2/min, find the rate at…

A:

Q: Water is flowing into a vertical cylindrical tank at the rate of 5 cu ft/min. If the radius of the…

A: Given, water is flowing into a vertical cylindrical tank at the rate of 5 cu ft/min (ie) Volume is…

Q: If a snowball melts so that its surface area decreases at a rate of 9 cm2/min, find the rate at…

A:

Q: side

A: Please refer to the image below

Q: The side of a cube increases at a rate of 2.5m/s. Find the rate at which the surface area increases…

A: As we know that; The expression of the surface area of the cube is: As=6a2        ....(1) Where;…

Q: The side of a cube decreases at a rate of 8 m/sec. Find the volume changes, when the side is 6 m. O…

A: Please refer the image.

Q: The side of a cube decreases at a rate of 7 m/sec. Find the rate at which the volume changes, when…

A:

Q: The volume of a cube decreases at a rate of 12.1 m/sec. Find the rate at which the side of the cube…

A: we have to find the rate change of a side of cube

Q: Find the surface area of a sphere at the instant when the rate of increase of the volume of the…

A:

Q: Sugar juice is filtering through a conical funnel 20cm deep and 12cm across the top into a…

A: Given that,Sugar juice is filtering through a conical funnel 20cm deep and 12cm across the top into…

Q: Sand is leaking through a small hole at the bottom of a conical funnel at the rate of 12rcm³ / s. If…

A: Given: Radius of the funnel r=8 cm. Height of the funnel h= 16 cm. rate of change of volume…

Q: The volume of a cube is increasing at the rate of 8 cm /sec.How fast is the surface area in creasing…

A: We can find the answer as below

Q: water is running out of a conical funnel at the rate of 1 cu inches per second. If the radius of the…

A: This question is related to application of derivatives.

Q: Find the rate of change of volume of a sphere with respect to its surface area when the radius is 2…

A:

Q: Find the rate at which the volume of a right circular cylinder of constant altitude 10 ft changes…

A:

Q: The radius of a sphere decreases at the rate of 4 m/sec. Find the rate at which the volume decreases…

A: Given  Radius = 4 m  Rate of decrease of radius = 5 m/sec

Q: at what rate is the volume of the cube changing if the edge is 8cm and is changing at 4cm/sec?

A: The volume of a cube is: Where, a is the edge of the cube. Formula used:

Q: The side of a cube increases at the rate of 1 m/sec. The rate at which the volume of the cube…

A:

Q: The volume of a sphere is increasing at a rate of 40 cm^3/sec. At what rate is the radius ofthe…

A:

Q: If the radius of a sphere is increasing at a constant rate of 3 cm/sec, then the volume is…

A:

Q: The side of a cube decreases at a rate of 9 m/sec. Find the rate at which the volume changes, when…

A: To find the rate of change of volume

Q: Water is running out of a conical funnel at the rate of 1 in3/ sec. If the radius of the base of the…

A:

Q: The side ofa cube increases at a rate of 10 m/sec. Find the rate at which the volume of the cube…

A:

Q: 1. The side of a cube increases at the rate of 12 m/sec. Find the rate at which the volume of the…

A: Our guidelines for multiple questions,answer only first question For other answers , Repost this…

Q: The volume of a cube is growing at a rate of 2 in3/min. Determine the rate at which the surface of…

A: Given:The volume of a cube is growing at a rate of 2 in3/min, that is dVdt=2 in3/min, where V is the…

Q: At a constant pressure, what temperature must be reached to increase the volume of a 100mL samples…

A:

Q: If the radius of a sphere increases at a rate of 0.5 m/sec, then the rate at which the volume of the…

A: Let the radius of the sphere be r. Then the volume of the sphere is: V=43πr3…

Q: Sand is leaking through a small hole at the bottom of a conical funnel at the rate of 12rcm³ /s. If…

A: Given-  dVdt=12π cm3sec.,R=8 cm and H=16 cm To find- depth of sand after 15seconds and the rate of…

Q: The side of a cube decreases at a rate of 10 m/sec. Find the rate at which the volume changes, when…

A: Differentiate volume of cube wrt t

Q: If a snowball melts so that its surface area decreases at a rate of lcm²/min, find the rate at which…

A: Snowball represents a sphere So , Surface Area of sphere is 4πr2.  And , d=2r.  Using this we solve…

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: The radius of a sphere decreases at a rate of 4 m/s. when the radius is 7 m, then the rate at which…

A:

Q: coffee is draining out of a conical filter at a rate of 2.25 inches cubed per minute. If the cone is…

A: given: coffee is draining out of a conical filter at a rate of 2.25 inches cubed per minute. If the…

Q: All the edges of a cube are expanding at a rate of 1/6 cm/sec. Determine the rate of change of the…

A:

Q: A snowball is being made so that its volume is increasing at the rate of 8 ft3/min. Find the rate at…

A: The geometrical figure of a snowball is a sphere. The volume of a sphere of radius r is V=4/3×πr3.…

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.