An open rectangular box measures externally 32 cm long, 27 cm wide and 15 cm deep. If the box is made of wood 1 cm thick, find the volume of wood used.
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The volume of a rectangular box is 1008 cm³ . If its length is 14 cm and its breadth is 9 cm, find its height.
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A pyramid has a square base ABCD of side 10 cm. The vertex V is 12 cm above the centre of the base E.
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i) Find the angle of inclination of VA to the horizontal.
ii) Calculate the volume of the pyramid.
Find the area of the curved surface of a cone whose base radius is 3 cm and whose height is 4 cm.
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Calculate the volume and surface area of a sphere of radius 210 cm
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Find the volume of the metal needed to make 1000 ball bearings of diameter 4 mm
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The surface area of a solid sphere whose radius is 6 cm is equal to the surface area of a solid right cylinder with radius of 2 cm. Find the height of the cylinder.
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ABCDV is a right square pyramid where ABCD is the square base with BC and AD being diagonals and V the vertex which is 6 cm vertically above the centre E of the base.
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(a) Draw a three dimensional diagram of the pyramid.
(b) Calculate:
i) the length BV
ii) the angle between the planes AVC and BVD
iii) the volume of the pyramid.
Sketch the graph of the function f(x) = −1 + |x| and find:
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i) the domain and
ii) the range, of f(x).
Find the domain and range of the relation y = 3x² + 2.
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