Shortcut Trick
Radius (r) = 30 ÷ 2 = 15 m, Height (h) = 8 m.
Using the Pythagorean triplet (8, 15, 17), the slant height (l) = 17 m.
Canvas required = Curved Surface Area = πrl
⇒ Area = 3.14 × 15 × 17 = 3.14 × 255 = 800.7
∴ The correct answer is 800.7 m2.
Alternate Method
Given:
Diameter of the base of the cone (d) = 30 m
⇒ Radius (r) = d ÷ 2 = 30 ÷ 2 = 15 m
Height of the cone (h) = 8 m
Value of π = 3.14
h = 8 m
r = 15 m
l = 17 m
Canvas Area = Curved Surface Area
Formula Used:
Slant height of a cone (l) = √(r2 + h2)
Curved Surface Area (CSA) of a cone = πrl
Calculations:
⇒ First, find the slant height (l) of the conical heap:
⇒ l = √(152 + 82)
⇒ l = √(225 + 64)
⇒ l = √289 = 17 m
⇒ The area of the canvas required to just cover the heap is equal to its Curved Surface Area.
⇒ Canvas required = πrl
⇒ Canvas required = 3.14 × 15 × 17
⇒ Canvas required = 3.14 × 255
⇒ Canvas required = 800.7 m2
∴ The correct answer is 800.7 m2.
Additional Information
Total Surface Area of a Cone
The total surface area includes both the curved surface and the flat circular base: TSA = πrl + πr2 = πr(l + r).
Volume of a Cone
The volume of a cone is exactly one-third the volume of a cylinder that has the same base radius and height: Volume = (1/3)πr2h.
Pythagorean Triplets
Using standard right-angle triangle triplets such as (3, 4, 5), (5, 12, 13), and (8, 15, 17) helps in quickly finding the missing side lengths in 2D and 3D geometry problems.