Multiple choice

A solid is in the form of a right circular cylinder mounted on a solid hemisphere of radius $14$ cm. The radius of the base of the cylindrical part is $14$ cm and the vertical height of the complete solid is $28$ cm. Find : (i) The volume of the solid (ii)The surface area of the solid (iii) Cost of painting the solid at the rate of Rs.$0.80$ per $cm^{2}$

  1. $\displaystyle 14373\frac{1}{3}\, cm^{3}$, $3080\, cm^{2}$, Rs. $2464$
  2. $\displaystyle 1473\frac{1}{2}\, cm^{3}$, $3582\, cm^{2}$, Rs. $2499$
  3. $\displaystyle 14573\frac{1}{5}\, cm^{3}$, $3810\, cm^{2}$, Rs. $2762$
  4. $\displaystyle 14370\frac{1}{7}\, cm^{3}$, $3087\, cm^{2}$, Rs. $2465$
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A Correct answer
Explanation

The cylinder height is 28 - 14 = 14 cm. Volume = (1/3)*pi*r^2*h_hemisphere + pi*r^2*h_cylinder = (2/3)*pi*14^3 + pi*14^2*14 = 14373.33 cm^3. Surface area = 2*pi*r^2 (hemisphere) + 2*pi*r*h (cylinder) = 2*pi*14^2 + 2*pi*14*14 = 3080 cm^2. Cost = 3080 * 0.80 = 2464.

AI explanation

The volume is the sum of the hemisphere volume and the cylinder volume, calculated as (2/3)pi(14^3) + pi*(14^2)*14, which equals 14373 1/3 cm cubed. The surface area only includes the curved surface of the hemisphere and the cylinder, calculated as 2*pi*14*14 + 2*pi*14*14, giving 3080 sq cm. Multiplying this area by the rate of Rs 0.80 gives a total cost of Rs 2464.

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