Question 1 An open flat-topped water trough in the shape of a triangular prism is emptied through a hole in its base at a constant rate of 16 litres per second. Its top measures 2 m by 4 m and its triangular end has a vertical height of 25 cm. When the water depth is h cm, the surface measures x cm by 4 m. (a) Show that when the depth of water is h centimetres, the volume V cm³ of water in the trough is given by V = 1600h² cm³. 25cm th 4m 2m
Question 1 An open flat-topped water trough in the shape of a triangular prism is emptied through a hole in its base at a constant rate of 16 litres per second. Its top measures 2 m by 4 m and its triangular end has a vertical height of 25 cm. When the water depth is h cm, the surface measures x cm by 4 m. (a) Show that when the depth of water is h centimetres, the volume V cm³ of water in the trough is given by V = 1600h² cm³. 25cm th 4m 2m
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Transcribed Image Text:Question 1
An open flat-topped water trough in the shape of a triangular prism is emptied
through a hole in its base at a constant rate of 16 litres per second. Its top
measures 2 m by 4 m and its triangular end has a vertical height of 25 cm.
When the water depth is h cm, the surface measures x cm by 4 m.
(a) Show that when the depth of water is h centimetres, the volume V cm³ of
water in the trough is given by V = 1600h² cm³.
(b) Find the rate at which the depth of water is changing when h=10 cm.
25ст
4m
2m
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