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Application Of Derivatives

Question

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An edge of a variable cube is increasing at the rate of 3 cm per second. How fast is the volume of the cube increasing when edge is 10 cm long?

Solution

Let x cm. be the length of an edge of a variable cube and V be its volume at any time t.

therefore space space space space space straight V space equals space straight x cubed space space space space space space space space space space space space space space space rightwards double arrow space space space space space dV over dt space equals space 3 straight x squared dx over dt

But

dx over dx space equals space 3 space cm divided by straight s

(given)

therefore space space space space space dV over dt space equals space 3 straight x squared.3 space equals space 9 straight x squared

When x = 10 cm,

dV over dt space equals space 9 cross times left parenthesis 10 right parenthesis squared space equals space 900 space cm cubed divided by straight s

∴ volume of the cube is increasing at the rate of 900 cm³/s when the edge is 10 cm long.

Some More Questions From Application of Derivatives Chapter

The radius of a circle is increasing uniformly at the rate of 4 cm per second Find the rate at which the area of the circle is increasing when the radius is 8 cm.

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