Home
Class 11
PHYSICS
If surface area of a cube is changing at...

If surface area of a cube is changing at a rate of `5 m^(2)//s`, find the rate of change of body diagonal at the moment when side length is `1 m`.

A

`5 m//s`

B

`5sqrt(3) m//s`

C

`5/2sqrt(3) m//s`

D

`5/(4sqrt(3)) m//s`

Text Solution

Verified by Experts

The correct Answer is:
C, D
Surface area of cube `S=6a^(2)` (where a=side of cube)
Body diagonal `1=sqrt(3)a`. Therefore `S=2l^(2)`
Differentiating it w.r.t. time `(dS)/(dt)=2(2l)(dl)/(dt)rArr (dl)/(dt)=(1)/(4(sqrt(3)a))(dS)/(dt)=5/(4sqrt(3)) m//s`
Promotional Banner

Topper's Solved these Questions

  • MISCELLANEOUS

    ALLEN |Exercise Part -II Example|61 Videos

  • MISCELLANEOUS

    ALLEN |Exercise Part -II Example Some worked out Examples|1 Videos

  • KINEMATICS (MOTION ALONG A STRAIGHT LINE AND MOTION IN A PLANE)

    ALLEN |Exercise BEGINNER S BOX-7|8 Videos

  • PHYSICAL WORLD, UNITS AND DIMENSIONS & ERRORS IN MEASUREMENT

    ALLEN |Exercise EXERCISE-IV|7 Videos

Similar Questions

Explore conceptually related problems

The volume of a cube is increasing at the rate of 8 cm^(3)//s . How fast is the surface area increasing when the length of an edge is 12 cm ?

The surface area of a spherical bubble is increasing at the rate of 2 c m^2//s . When the radius of the bubble is 6cm, at what rate is the volume of the bubble increasing?

The area of a triangle is increasing at the rate of 4 cm^(2)//s . Its altitude is increasing at the rate of 2 cm/s. When the length of its altitude is 20 cm and its area is 30 cm^(2) , find the rate of change of its base.

The rate of change of surface area of a sphere w.r.t. radius is ………..

The total surface area of a cube is 1350 sq.m Find its volume.

The radius of a circle is increasing uniformly at the rate of 3 cm/s. Find the rate at which the area of the circle is increasing when the radius is 10 cm.

An edge of a variable cube is increasing at the rate of 10 cm/s. How fast the volume of the cube is increasing when the edge is 5 cm long?

Radius of a spherical balloon is increasing with respect to time at the rate of 2//pi" "m//s . Find the rate of change in volume (in m^(3)//s ) of the balloon when radius is 0.5 m?

If the height of the cone is constant then find the rate of change of its curved surface area with respect to its radius.

The area of an expanding rectangle at the rate of 48cm^(2)//s. the length of rectangle is always equal to square of the breadth. At which rate the length is increasing at the instant when th ebreadth is 4 cm?