An ice cream cone has a radius of 2 cm and slant height of 5 cm. If 100 such cones are to be painted externally (excluding base), what is the total painted area?
3140 cm2
Painting a cone “externally, excluding the base” means only the slanting curved surface of the cone gets paint; the flat circular base is left out.
The curved (lateral) surface area of a cone is \(\text{CSA} = \pi r l\), where \(r\) is the base radius and \(l\) is the slant height.
Here \(r = 2\ \text{cm}\) and \(l = 5\ \text{cm}\), and we take \(\pi = 3.14\).
CSA of one cone \(= 3.14 \times 2 \times 5 = 3.14 \times 10 = 31.4\ \text{cm}^2\).
There are 100 such cones, so total painted area \(= 100 \times 31.4 = 3140\ \text{cm}^2\).
Key concept: for painting an open cone use only \(\pi r l\) (curved surface), never the total surface area \(\pi r(l+r)\), since the base is excluded.
Hence the total painted area is 3140 cm2.
Similar Questions
A manufacturer reduces the diameter of their spherical bearing balls by 50% to cut costs. What is the percentage decrease in volume of each ball?
A small temple dome is shaped like a hemisphere of radius 3.5 m. How much area (in square meters) must be painted on the curved surface?
In a manufacturing plant, a cone-shaped part has a curved surface area of 330 cm² and a base radius of 7 cm. What is its height?
A sphere is tightly enclosed inside a cube of side length a. If the cube is then inscribed inside another sphere, what is the ratio of the inner to outer sphere volumes?
A right circular cone has a height of 12 cm and a radius of 5 cm. Find its slant height and curved surface area.
A solid metallic sphere of radius R is heated so that its radius increases by 10%. Find the approximate percentage increase in its volume.
Two identical regular right pyramids, each with a square base of side 6 cm and a perpendicular height of 4 cm, are stacked one on top of the other such that their bases perfectly align. The top pyramid is inverted. Calculate the slant height of a single pyramid.
The base of a regular right pyramid is an isosceles triangle with equal sides of 25 cm and a base of 30 cm. The slant height of the pyramid is 40 cm. Find the total surface area of the pyramid.
If the lateral surface area of a right circular cylinder is equal to twice the area of its base, find the height in terms of the radius.
If the surface area of a sphere increases by 44%, by what approximate percent does the radius increase?
Important Questions from Solid Figures
A cone and a hemisphere have equal bases and volumes. What is the ratio of the height of the cone to the radius of the hemisphere?
If the surface area of a sphere is 64 π cm 2, then the volume of the sphere is:
Find the surface area of a sphere of diameter 21 cm. (Use π = \(\frac{{22}}{7}\) )
A cube is 7 cm of an edge and another cube is 14 cm on an edge. The ratios of their surface areas are
Using three distinct points which of the following shapes cannot be formed?
