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Geometry Level 1

A wooden toy in the form of a cone surmounted on a hemisphere. The diameter of the cone is 6cm and its height is 4 cm. Find the cost of painting the toy at a rate of Rs 5 per 1000 sq cm


The answer is 0.51.

Baranee Tharan by Baranee Tharan , 25, India

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1 solution

The surface area of the compound figure is given by A = 1 2 c L + 1 2 ( 4 π r 2 ) A=\dfrac{1}{2}cL+\dfrac{1}{2}(4\pi r^2) where c c is the circumference of the base of the cone, r r is the radius, L L is the slant height. Substituting, we get

A = 1 2 ( 2 π ) ( 3 ) ( 5 ) + 2 π ( 9 ) = 33 π A=\dfrac{1}{2}(2\pi)(3)(5)+2\pi (9)=33 \pi

The desired cost is therefore

c o s t = 33 π ( 5 1000 ) ≈ 0.518362787 cost= 33\pi \left(\dfrac{5}{1000}\right) \approx \boxed{0.518362787}

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