CUBES
A cube is a solid of uniform cross-section. It is formed by squares and has 8 vertices. An example is processed cubed sugar.
The length of a side of a cube is ‘e’ which is the length of all sides since a cube is formed with squares.
TOTAL SURFACE AREA OF A CUBE
A cube has 6 faces. The surface area of each side = e2 as each side is a square.
Therefore, Total surface area of a cube (all 6 sides) = 6e2
The surface area of a cube is gotten by the formula
Surface area= 6e2 sq. units
VOLUME OF A CUBE
In a cube all sides are equal. Length=e, height=e and width=e
Therefore, Volume of a cube= length× width× height
Volume of a cube= e3 cubic units
CYLINDERS
A Cylinder is a uniform circular cross-section. Examples of cylinders are unsharpened pencils like HB or 2B pencils, garden rollers, tins of milk or tomato et cetera
TOTAL SURFACE AREA OF A CYLINDER
There are two types of cylinders;
(1) A closed cylinder and
(2) An open cylinder
TOTAL SURFACE AREA OF A CLOSED CYLINDER
The total surface area of a closed cylinder consists of a sum of the areas of (i) the curve surface and (ii) The two circular end faces.
The curved surface when opened out is a rectangle. This rectangle has length equal to the length of the
Cylinder and the width are equal to the circumference of the circular end face.
Area of curved surface of a cylinder = area of rectangle of dimensions length (L) and width
(Circumference of base)
= 2πrl
Area of the two circular end faces= twice the area of one circular face
= πr2
Hence the total surface area of the closed cylinder
= 2πrl + 2πr2 sq. units
TOTAL SURFACE AREA OF AN OPEN CYLINDER
The total surface area of an open cylinder is the area of the curved surface which is the area of the rectangle the cylinder forms when spread.
Sometimes we are given a thick hollow cylinder. The total surface area is the sum of;
(i) the area of the external curved surface
(ii) the area of the internal curved surface and
(iii) the area of the end annular faces which will be shaded…
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