9. When a particular plate of metal is heated in an oven, its radius increases at the rate of 0.01cm/min. At what rate is the plate's area increasing when the radius is 10cm?

Q: 7. A triangle with a base of 20 inches has a height that is decreasing at a rate of 3 inches per…

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Q: 4. A stone dropped in a pond sends out a circular ripple whose radius increases at a constant rate…

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Q: Water is poured into a conical paper cup at the rate of 3/2 in/sec (similar to Example 4 in Section…

A: I will use the formula V=13πr2h and differentiation method to solve this problem.

Q: 1. A paper cup has the shape of a cone with height 12 cm and radius 4 cm (at the top). If water is…

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: 7) A spherical balloon is to be deflated so that its radius decreases at a constant rate of 15…

A: Given: A spherical balloon is to deflated so that its radius decreases at a constant rate of 15…

Q: 1. Water is flowing at the rate of 2 m3/min into a tank in the form of an inverted cone having an…

A: It is given that the cone has altitude 16 m and radius 4 m. That is, hcone=16,rcone=4. Let r and h…

Q: 8. If a snowball melts so that its surface area decreases at a rate of 4 cm2 /min , find the rate at…

A:

Q: 2. A balloon in the shape of a sphere is being inflated at the rate of 100 cm/sec. a. At what rate…

A: a)  Given that the balloon is in the shape of sphere and it is being inflated at the rate of…

Q: 1. A boy is blowing a spherical balloon at a rate of 50 cm /s. At what rate is the radius of the…

A: This question is based on application of derivative.

Q: Water is dripping into a hemispherical bowl with a radius of 8 cm at a rate of 1 cubic cm per…

A:

Q: 8. The volume of a right circular cylinder is 60 cm³ and is increasing at 2 cm³/min at a time when…

A: Given:                                 Volume of a right circular cylinder V…

Q: 13. A plane flying horizontally at an altitude of 1 mi and a speed of 500 mi/h passes directly over…

A:

Q: 1. The sides of a square decrease in length at rate 2 m/sec. At what rate is the area of the square…

A:

Q: 11. A snowball melts so that its surface area decreases at a rate of 0.5 cm/min. Find the rate at…

A:

Q: 8. The radius of an inflating balloon in the shape of a sphere is changing at a rate of 3cm/sec. At…

A:

Q: A cylindrical column is (3m) high and (0.2m) radius, if the radius of the column increases at a rate…

A:

Q: 1. Water is poured into a conical tank 6 m across the top and 8m deep at the rate of 10 How fast is…

A: To find: The rate of water level rising when water in the tank is 5 m deep. Formula used: The volume…

Q: A spherical balloon is being deflated at a rate of 80 cm3/min. At what rate is the radius decreasing…

A:

Q: a) When a gold plate is heated in order to melt it, initially its area increases at the rate of 67…

A:

Q: 9) A spherical snowball is melting in such a way that its volume is decreasing at a rate of 3cm /…

A: Let, r=radius  V=volume Given that dV/dt= 3 , we have to find dr/dt=? at r=12 cm Volume and radius…

Q: Find the rate of change. Volume of a cube with respect to its sides when s = 5

A: The volume of a cube with side s is V=s3 Differentiate with respect to s dVds=ddss3=3s2

Q: The radius of an bubble is increasing at the rate of 1/2 cm/s. At what rate is the volume of the…

A: Here  radius of bubble is given and rate of change of radius of bubble is also given

Q: How fast is the surface area of a circular oil spill in the ocean changing when the radius is 10ft…

A:

Q: 5. The volume of a cube is increasing at a rate of 10 cm³/min . How fast is the surface area…

A: Given:- The volume of a cube is increasing at a rate of 10 cm³/min. To find:- How fast is the…

Q: The original 24 m edge length x of a cube decreases at the rate of 5 ​m/min.   a. When x=5m, at what…

A:

Q: The sides of a square increase in length at a rate of 4 m/sec. a. At what rate is the area of the…

A: Area of square = a2 Where a is length of side of square.

Q: 1. A spherical balloon is being inflated so that the volume is increasing at the rate of 5 ft.³ per…

A:

Q: 16. If the radius of a circle is increasing at the rate of 4 cm/s, find the rate of the increase in…

A: Given radius of a circle is increasing at the rate of 4 cm/sec.

Q: A vertical cylinder is leaking water at a rate of 8m^3/sec. if the cylinder has a height of 10m and…

A: In a vertical cylinder water is leaking at a rate of 8 m3/sec. dVdt=8 Height of the cylinder is 10…

Q: A perfectly spherical balloon is losing volume at a rate of 3 in3 per sec. How fast is the balloon’s…

A:

Q: The original 24 m edge length x of a cube decreases at the rate of 2 m/min. a. When x = 1 m, at what…

A:

Q: 20. The length of a rectangle is increasing at a rate of 5 cm/sec and the width is decreasing at a…

A:

Q: When a circular plate is heated on an oven its radius increases at a rate of 0.03 cm/ min at what…

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Q: 7. A spherical balloon is being filled in such a way that the surface area is increasing at a rate…

A:

Q: 14. If a snowball melts so that its surface area decreases at a rate of 1 cm2/min, find the rate at…

A: To find the rate

Q: When a circular plate of metal is heated in an oven, its radius increases at the rate of 0.01 cm…

A: Given:When a circular plate of metal is heated in an oven, its radius increases at the rate of 0.01…

Q: 3. The volume of a cube is increasing at the rate of 6 cm³/min. How fast is the surface increasing…

A:

Q: 2. The radius of a sphere is decreasing slowly at the rate of 2 cm/week. How fast is the volume…

A: Consider the given information. The volume of the sphere is defined as, V=43πr3

Q: 11. At what rate is the volume of the cube changing if the edge is 8 cm and is changing at 4 cm/s?

A: As we know that; The expression for the volume of the cube with the edge length ''a'' is: v=a3…

Q: The original 24 m edge length x of a cube decreases at the rate of 2 m/min. a. When x = 4 m, at what…

A: As Given :                   The length x of Cube decrease at a rate of 2 m/min.…

Q: 1. A spherical balloon is expanding. If the radius is increasing at the rate of 2 inches per minute,…

A: The given question can be solved as shown in step2.

Q: 4. A spherical balloon is to be deflated so that its radius decreases at a constant rate of 15…

A:

Q: as a balloon in the shape of a sphere is being blown up, the volume is increasing at the rate of 4…

A: Volume of the sphere Shape ballon: V = 4/3ℼr3   (r = radius)   Now differentiate with respect to L,…

Q: 7. A vertical cylinder is leaking water at a rate of 1 ft'/sec. If the cylinder has a height of 10…

A: To find the rate of change of height of water changing

Q: 3. The area of a circular inkblot starts from zero and grows at a constant rate of 4n cm/minute.…

A: Use the derivative and formula for area of circle.

Q: 1. When a circular plate of metal is heated in an oven its radius increases at a rate of 0.01…

A:

Q: Suppose that a spherical balloon is being inflated and the radius of the balloon is increasing at a…

A:

Q: 2. The diagonal of a square increases at the rate of 3 m/sec. How fast is the area changing when the…

A: Let the length of diagonal be y. so that, Now, Length of the side of a square be x. Using the…