A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.4 cm/min. At what rate is the volume of the snowball decreasing when the radius is 15 cm. (Note the answer is a positive number). cm3 min 4 Hint: The volume of a sphere of radius r is V

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: Air is being pumped into a spherical balloon so that its volume increases at a rate of 2…

A:

Q: A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.4 cm/min.…

A:

Q: A hemispherical tank with a radius of 8 m is filled from an inflow pipe at a rate of 5 m / min (see…

A:

Q: 2. The edge of a cube decreases at a rate of 2.5m/s. Find the rate at which the surface area…

A: Application of derivatives.

Q: How fast is the volume of a sphere changing when the radius is 20 cm if the radius is changing at…

A: We will find the rate of change of volume of sphere at a given radius.

Q: Air is being pumped into a spherical balloon at a rate of 4.5 cubic inches per minute. How fast is…

A:

Q: A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.3 cm/min.…

A:

Q: Air is being pumped into a spherical balloon so that its volumeincreases at a rate of 100 cu. cm /s…

A:

Q: A rectangular prism with dimensions 6 m x 4 m x 8 m ( x w x h) is shrinking. 8 m 4 m 6 m Answer the…

A: Here volume of the prism will be V=lbh So the change in volume in time t will be given by…

Q: A hemispherical tank with a radius of 9 m is filled from an inflow pipe at a rate of 3 m / min (see…

A:

Q: A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.3 cm/min.…

A:

Q: Q3) the radius of the base and high of right circular cone at given instant (t ) are r 20cm and…

A: Volume of a cone = 13πr2hVolume r→radius and h→ height∴V = 13πr2h   dvdt =13πddtr2h   dvdt =…

Q: A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.1 cm/min.…

A:

Q: A spherical snowball is melting in such a way that its radius is decreasing at rate of 0.4 cm/min.…

A: The radius of a snowball is decreasing at a rate of 0.4 cm/min. We need to find at what rate the…

Q: A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.3 cm/min.…

A:

Q: The radius of a right circular cone increases at a rate of 1.8 in / s, while its height decreases at…

A: To find the rate of change of volume

Q: The radius of a sphere is decreasing at a rate of 1/4 cm/s. At what rate is the volume decreasing if…

A: Volume of the sphere , V=43πr3

Q: 19. A conical glass whose radius is 5m and altitude 12m is being filled at the rate of 10 m. How…

A: For conical glass, Radius r=5 m, Height h=12 m, Rate of filling dVdt=10 cm3/s.

Q: Suppose a spherical balloon grows in such a way that after t seconds, its volume V is given by V = 4…

A:

Q: A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.1 cm/min.…

A: We will find the required.

Q: A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.4 cm/min.…

A:

Q: A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.3 cm/min.…

A: The question is from the Application of Derivatives

Q: The volume of a sphere is expanding where r= 2t + 1. What is the rate of change in volume with…

A:

Q: Sand is poured onto a surface at 11 cm³/sec, forming a con- ical pile whose base diameter is always…

A:

Q: A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.2 cm/min.…

A: The volume of a sphere of radius  r unit is given by the relationship ; V=43πr3 And the rate of…

Q: A potter forms a piece of clay into a right circular cylinder. As she rolls it, the height h of the…

A: Here, given that the volume is constant. So, dVdt=0⇒ddtπr2h=0⇒πh 2rdrdt+r2dhdt=0⇒h 2rdrdt+r2dhdt=0…

Q: The radius of a sphere decreases at a rate of 3 m/s. when the radius is 9 m, then the rate at which…

A:

Q: The spherical balloon is being filled at a constant rate of 3cm/sec. How fast is the radius…

A:

Q: A raindrop is a perfect sphere with radius r cm and surface area S. Condensation accumulates on the…

A:

Q: Air is being pumped into a spherical balloon so that its volume increases at a rate of 70cm³ /s. How…

A: Volume of the sphere , V =43πr3 ; where , 'r' is the radius of the sphere. Surface Area of the…

Q: A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.2 cm/min.…

A: Using, Volume of a sphere of radius r is V =…

Q: : B1. The radius of a sphere increases at the rate of 4 m/sec. Find the rate at which the volume of…

A: We have to find the rate of volume increase.

Q: A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.2 cm/min.…

A: We have to find the rate of decreasing of volume.

Q: A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.4 cm/min.…

A:

Q: 3. A square is expanding in such a way that its diagonal is increasing at the rate of 2 in/s. (a) At…

A: Diagonal of Square = √2 * Side Perimeter of Square = 4* Side Area of Square = (Side)^ 2

Q: The Volume of a Sphere is increasing at the rate of 8 m³; how fast is its Radius increasing when the…

A:

Q: Suppose that a tumor in a person's body has a spherical shape and that treatment is causing the…

A:

Q: B. The dimensions of a rectangular solid at a given instant (to) are (a = 13 cm), (b = 9 cm) and (c…

A:

Q: 2. The edge of a cube decreases at a rate of 1.5m/s. Find the rate at which the surface area…

A: Solution Calculate the area of cube

Q: A snowball is rolling down a hill. As the snowball rolls, it picks up more snow and gets larger. If…

A:

Q: A spherical snowball is melting in such a way that its radius is decreasing at rate of 0.2 cm/min.…

A: We know that volume of spherical snowball V=43πr3 Differentiate w.r.t.'t'…

Q: A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.4 cm/min.…

A:

Q: A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.1 cm/min.…

A:

Q: 18 Show that the volume V of a regular tetrahedron, all of whose side lengths are s, is V = s°V2…

A: Given that the volume of a tetrahedron is: 1442cm3 So, V=112s32 So, 112s32=1442⇒s3=123⇒s=12

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

A: Let the side of the cube be x meter at time t  So, it is given that, dx/dt = 10 And, the volume of…

Q: Sand is dumped in such a way that the shape of the sand pile is always a cone with its height, h…

A: Let, h be the height of the cone, r be the radius of the cone. Also, the sand is dumped at a…

Q: Q3: A right circular cone has the radius of the base and the height which at a given instant (to)…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.