Surface Area

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Surface Area

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Surface area is the measure of how much exposed area a solid object has, expressed in square units. Mathematical description of the surface area is considerably more involved than the definition of arc length of a curve. Surface Area

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Euclid in 300 BC, also known as Euclid of Alexandria, was a Greek mathematician and is often referred to as the "Father of Geometry." He was active in Hellenistic Alexandria during the reign of Ptolemy I (323–283 BC). His Elements is the most successful textbook and one of the most influential works in the history of mathematics, serving as the main textbook for teaching mathematics (especially geometry) from the time of its publication until the late 19th or early 20th century.In it, the principles of what is now called Euclidean geometry were deduced from a small set of axioms. Euclid also wrote works on perspective, conic sections, spherical geometry, number theory and rigor. Father Of Geometry

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A cylinder A cube A sphere A cuboid 3-D shapes

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3-D stands for three-dimensional. 3-D shapes have length, width and height. For example, a cube has equal length, width and height. Face Edge Vertex How many faces does a cube have? 6 How many edges does a cube have? 12 How many vertices does a cube have? 8

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a cube of length l. All six faces of a cube have the same area. The area of each face is l × l = l2 Therefore, Cube

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A cuboid has 6 faces. Cuboid

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To find the surface area of a shape, we calculate the total area of all of the faces. The top and the bottom of the cuboid have the same area.

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The front and the back of the cuboid have the same area.

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The left hand side and the right hand side of the cuboid have the same area.

Formula for the surface area of a cuboid : 

We can find the formula for the surface area of a cuboid as follows. Surface area of a cuboid = Formula for the surface area of a cuboid = 2lb + 2bh + 2lh = 2(lb+bh+lh)

Using nets to find surface area : 

It can be helpful to use the net of a 3-D shape to calculate its surface area. Using nets to find surface area Here is the net of a 3 cm by 5 cm by 6 cm cuboid. Write down the area of each face. 15 cm2 15 cm2 18 cm2 30 cm2 30 cm2 18 cm2 Then add the areas together to find the surface area. Surface Area = 126 cm2

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A sphere is a body bounded by a surface whose every point is equidistant (i.e. the same distance) from a fixed point, called the centre. For example, a shot (a heavy iron ball) is a solid sphere and a tennis ball is a hollow sphere. One-half of a sphere is called a hemisphere. Sphere

Archimedes discovered that a cylinder that circumscribes a sphere, as shown in the following diagram, has a curved surface area equal to the surface area, S, of the sphere. : 

Archimedes discovered that a cylinder that circumscribes a sphere, as shown in the following diagram, has a curved surface area equal to the surface area, S, of the sphere.

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base altitude radius Cylinder

What will happen if we removed the end of the cylinder and unrolled the body? : 

What will happen if we removed the end of the cylinder and unrolled the body?

This will happen if we unrolled and removed the end of a cylinder…. : 

This will happen if we unrolled and removed the end of a cylinder…. Circumference of the base h 2Πr2

Notice that we had formed 2 circles and a 1 rectangle…. : 

Notice that we had formed 2 circles and a 1 rectangle…. The 2 circles serves as our bases of our cylinder and the rectangular region represent the body

How can we solved the surface area of a Cylinder? : 

How can we solved the surface area of a Cylinder? To solve the surface area of a cylinder, add the areas of the circular bases and the area of the rectangular region which is the body of the cylinder.

This is the formula in order to solved the surface area of a cylinder. : 

This is the formula in order to solved the surface area of a cylinder. Surface Area = area of 2 circular bases + area of a rectangle =2Πr2 +2Πr =2Πr (r + h) __________ __________

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Thanks Teachers in charge : Beena Sharitha

Reference : 

Reference Wikipedia Students Maths Maths Teachers

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Prepared by : Pradeep Sajeev

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