Maths question from Social Forest Worker exam, 2026 by JKSSB
A wooden toy is shaped like a rocket with a cone mounted on a cylinder. The total height of the rocket is 26 cm, while the height of the conical part is 8 cm. The base of the conical portion has a diameter of 12 cm, while the base diameter of the cylindrical portion is 6 cm. The conical portion is to be painted orange and the cylindrical portion yellow. Calculate the total cost of painting the orange portion in terms of a, if the cost of painting is 0.1 Rs per mm².
Last updated Jul 21, 2026
Correct Answer:
Option A —
870π
The correct option is A) 870π.
Explanation
To find the total cost of painting the orange portion, we first find the total surface area of the cone exposed to be painted, convert it to square millimeters, and multiply by the unit cost:
Dimensions of the Cone:
Radius of the cone base is six centimeters (half of twelve centimeters).
Height of the cone is eight centimeters.
Using the Pythagorean relationship, the slant height is ten centimeters.
Surface Area of the Orange Region:
Curved surface area of the cone equals six multiplied by ten multiplied by pi, which is sixty pi square centimeters.
Base area of the cone equals six squared multiplied by pi, which is thirty-six pi square centimeters.
Base area of the attached cylinder equals three squared multiplied by pi, which is nine pi square centimeters.
The exposed base area around the cylinder is thirty-six pi minus nine pi, which equals twenty-seven pi square centimeters.
Total exposed orange surface area is sixty pi plus twenty-seven pi, which equals eighty-seven pi square centimeters.
Converting Units and Calculating Cost:
Since one square centimeter equals one hundred square millimeters, eighty-seven pi square centimeters equals eight thousand seven hundred pi square millimeters.
Multiplying eight thousand seven hundred pi square millimeters by zero point one Rupees per square millimeter gives a total cost of eight hundred seventy pi Rupees.
Answer verified by Quintessence Classes faculty — Karan Nagar, Srinagar.
