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Mensuration - volume

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A toy consists of a cylinder of diametre 6 cm 'sandwiched' between a hemisphere and a cone of the same diameter. If the cone is of height 8cm and a cylinder is of height 10cm, what is the volume of the toy.

Jeffreymars16  Jun 1, 2017
edited by Jeffreymars16  Jun 1, 2017
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r   =   6/2   =   3

volume of toy = volume of hemisphere + volume of cylinder + volume of cone

volume of toy = $$\frac12*\frac43*\pi*r^3$$ ) + ( $$\pi*r^2*\text{cylinder height}$$ ) + ( $$\frac13*\pi*r^2*\text{cone height}$$ )

volume of toy = $$\frac12*\frac43*\pi*3^3$$ ) + ( $$\pi*3^2*10$$ ) + ( $$\frac13*\pi*3^2*8$$ )

volume of toy = $$\frac12*\frac43*\pi*27$$ ) + ( $$\pi*9*10$$ ) + ( $$\frac13*\pi*9*8$$ )

volume of toy = $$18\pi$$ ) + ( $$90\pi$$ ) + ( $$24\pi$$ )

volume of toy = 132π   cubic centimeters               ≈ 414.69 cubic cm

hectictar  Jun 1, 2017