The outer curved surface of a hemispherical dome of a library is to receive two coats…
MATHEMATICS · Multi-part · CBSE · Mathematics · Surface Areas and Volumes · Surface Areas and Volumes
Problem
The outer curved surface of a hemispherical dome of a library is to receive two coats of whitewash. The contractor has 64\,kg of whitewash. One kilogram of this whitewash covers 2\,m2 of surface in a single coat.
(i) Write an equation in the radius r (in metres) of the dome that expresses the condition on the quantity of whitewash available for the two coats.
(ii) Solve the equation to find the radius of the dome correct to two decimal places, taking π=3.14.
(iii) If labour charges are Rs\,14 per square metre per coat, calculate the total labour cost for completing the work.