To find the total surface area of a cone, add its curved surface area (πrl) and base area (πr²). With a slant height of 21 m and a diameter of 24 m (radius 12 m), the total surface area is π × 12 × 21 + π × 12². This equals 252 π + 144 π = 396π m², approximately 1243.76 m² using π ≈ 3.14.

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Introduction to Cone Surface Area Calculation

Understanding the total surface area of a cone is a fundamental aspect of geometry. This calculation is crucial in various practical applications, from architectural design to manufacturing. The total surface area of a cone includes both the curved surface and the base area.

Formula for Total Surface Area

The total surface area of a cone is calculated by adding the curved surface area and the base area. The curved surface area is given by the formula πrl, where r is the radius and
l is the slant height. The base area is calculated using the formula πr², where r is the radius of the base.

Given Dimensions
In this specific problem, we are given the slant height of the cone as 21 meters and the diameter of its base as 24 meters. The diameter is the total distance across the circle forming the base of the cone.

Calculating the Radius

To proceed with the calculation, we first need to find the radius of the base. The radius is half of the diameter. Therefore, for a cone with a diameter of 24 meters, the radius r is 12 meters.

Applying the Formulas

With the radius and slant height known, we apply the formulas for the curved surface area (π × 12 × 21) and the base area (π × 12²). Adding these two areas gives us the total surface area of the cone.

Final Calculation and Result

The total surface area is thus 252 π + 144 π = 396 π square meters. Using the approximation π ≈ 3.14, the total surface area is approximately 1243.76 square meters. This calculation is essential for accurate material estimation in real-world applications.

Discuss this question in detail or visit to Class 9 Maths Chapter 11 for all questions.
Questions of 9th Maths Exercise 11.1 in Detail

Diameter of the base of a cone is 10.5 cm and its slant height is 10 cm. Find its curved surface area.
Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 24 m.
Curved surface area of a cone is 308 cm² and its slant height is 14 cm. Find (i) radius of the base and (ii) total surface area of the cone.
A conical tent is 10 m high and the radius of its base is 24 m. Find (i) slant height of the tent. (ii) Cost of the canvas required to make the tent, if the cost of 1 m² canvas is ₹70.
What length of tarpaulin 3 m wide will be required to make conical tent of height 8 m and base radius 6 m? Assume that the extra length of material that will be required for stitching margins and wastage in cutting is approximately 20 cm (Use π = 3.14).
The slant height and base diameter of a conical tomb are 25 m and 14 m respectively. Find the cost of white-washing its curved surface at the rate of ₹210 per 100 m².
A joker’s cap is in the form of a right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make 10 such caps.
A bus stop is barricaded from the remaining part of the road, by using 50 hollow cones made of recycled cardboard. Each cone has a base diameter of 40 cm and height 1 m. If the outer side of each of the cones is to be painted and the cost of painting is ₹12 per m², what will be the cost of painting all these cones?

Last Edited: January 2, 2024