Question

Pip is planning to make conical party hats. The conical hats are as shown in the diagram below, where \( h \) equals the height of the cone and \( r \) is equal to the radius of base of the cone. All measurements are in centimetres. a Express \( r \) in terms of \( h \) and hence show that the volume \( \left(V \mathrm{~cm}^{3}\right) \) of the cone \( \mathrm{i} \) terms of its height \( (h) \) is \( V=\frac{1}{3} \pi\left(100 h-h^{3}\right) \). Sketch the graph of \( V \) against \( h \) over an appropriate domain. Find the volume the cone if the height is \( 7.5 \mathrm{~cm} \). Pip wants the volume of the hats to be as large as possible. Find \( \frac{d V}{d h} \).

          Pip is planning to make conical party hats. The conical hats are as shown in the diagram below, where \( h \) equals the height of the cone and \( r \) is equal to the radius of base of the cone. All measurements are in centimetres.
a Express \( r \) in terms of \( h \) and hence show that the volume \( \left(V \mathrm{~cm}^{3}\right) \) of the cone \( \mathrm{i} \) terms of its height \( (h) \) is \( V=\frac{1}{3} \pi\left(100 h-h^{3}\right) \).

Sketch the graph of \( V \) against \( h \) over an appropriate domain.

Find the volume the cone if the height is \( 7.5 \mathrm{~cm} \).
Pip wants the volume of the hats to be as large as possible.

Find \( \frac{d V}{d h} \).

Pip is planning to make conical party hats. The conical hats are as shown in the diagram below, where h equals the height of the cone and r is equal to the radius of base of the cone. All measurements are in centimetres.
a Express r in terms of h and hence show that the volume (V cm^3) of the cone i terms of its height (h) is V=(1)/(3)π(100 h-h^3).

Sketch the graph of V against h over an appropriate domain.

Find the volume the cone if the height is 7.5 cm.
Pip wants the volume of the hats to be as large as possible.

Find (d V)/(d h).

Added by Brittany W.

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