Mathematics Kenya
Surface Area of Solids
A group of related sciences, including algebra, geometry, and calculus, concerned with the study of number, quantity, shape, and space and their interrelationships by using a specialized notation
Surface Area of Solids
Surface Area of Solids
Surface area of prisms, pyramids, cones, frustrums and spheres
Surface Area of a Right Circular Cone
A right circular cone is a cone whose vertex is vertically above the centre of the base of the cone.
Area of circular base =Πr2 (it is an area of a circle)
and the area of the sector (which is part of the part of a circle of radius ‘s’ and arc length (same as circumferance of the base) =2πr) = πs2 x r/s = πrs
Therefore the total surface area of a right circular cone =Πr2 +Πrs = Πr (r + s)
Example 6
Find the total surface of right circular cone whose slant light is 10cm and whose base radius is 8cm.Use Πr(r +s)
Example 7
Find the total surface area of a cone with diameter 8m and slant height of 10m. Use Π= 3.14
Surface Area of A Right Cylinder
If you want to know the amount of the covering the surface of a blue band margarine can, then you are finding the surface area of a right cylinder. Total surface area of the can is the sum of the areas of the top and bottom. Circular surfaces plus the area of the curved surface,
Now, consider a right cylinder of radius r and height h.
If the cylinder is opened up, the curved surface flattens out to form a rectangle. The length of the rectangle is 2Πr(the circumference of the circular base) and the width is h (the height of the cylinder).
Total surface area of cylinder:
Example 8
Find the total surface area of a cylinder with radius of 3m and height of 10m. Use Π= 3.14
Surface Area of a Right Pyramid
A right pyramid is one in which the slant edges joining the vertex to the corner of the base are equal
Example 9
A right rectangular pyramid is such that the rectangle is 12cm by 8cm and each slant edge is 12cm. Find the total surface area of the pyramid.
Surface Area of a Right Prism
A full brick or concrete block is an example of a right rectangular prism
Surface Area = Total or sum of the areas of each face.
A right prism is a prism in which each of the vertical edges is perpendicular to the plane of the base.
The figure above shows a rectangular right prism in which there are 6 faces though only three of them can be seen easily.
Generally for any right prism,
Example 10
The height of a right prism is 4cm and the perimeter of its base is 30cm. Find the area of its lateral surface.
Example 11
Find the total surface area of a rectangular prism 12 by 8 by 6 cm high.
The Formulae to Calculate the Surface Area of Spheres
Surface Area of a Sphere
The figure above shows a sphere (ball) with radius “r”
The surface area of a sphere is four times the area of circle with the same radius. The area of a circle is Πr2. Hence, the surface area of sphere is equal to 4Πr2.
Example 12
Find the surface area of a sphere of radius 5cm. (Π= 3.14)
Example 13
Find the surface area of a tennis ball, given that its radius is 3.3cm. UseΠ= 3.14 Express your answer to the nearest tenth.
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