3.6 Differentiation (A-level only)

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Question 12

A large conical salt pile is forming in a storage facility. Due to a height-limiting baffle, the pile maintains a fixed height of 12 metres. The base radius of the pile is $r\,$ metres and its slant height is $l\,$ metres.

Determine an expression for $l\,$ in terms of $r$ .

[1]

The pile is growing such that its base radius is increasing at a constant rate of 1.5 metres per hour.

Find the rate at which the total surface area of the salt pile is changing at the instant the radius is 5 metres. Give your answer in $m2\text{m}^2$ per hour to one decimal place.

[The total surface area, $S$ , of a cone is given by $\pi r^2 + \pi rl$ ]

[6]

Determine an expression for $l\,$ in terms of $r$ .

[1]

The pile is growing such that its base radius is increasing at a constant rate of 1.5 metres per hour.

Find the rate at which the total surface area of the salt pile is changing at the instant the radius is 5 metres. Give your answer in $m2\text{m}^2$ per hour to one decimal place.

[The total surface area, $S$ , of a cone is given by $\pi r^2 + \pi rl$ ]

3.6 Differentiation (A-level only)

Question 12

Markscheme

3.6 Differentiation (A-level only)

Question 12

Markscheme

3.6 Differentiation (A-level only)

Question 12

3.6 Differentiation (A-level only) Questions

3.6 Differentiation (A-level only)

Question 12

3.6 Differentiation (A-level only) Questions