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Surface Area and Volume of a Shape
Transcript of Surface Area and Volume of a Shape
What is surface Area? Surface Area is the area required to cover 3 Dimensional shape. What is volume? Volume is the amount space occupied by the 3 Dimensional shape. Or Number of unit cubes that will fit into a 3 Dimensional shape. How do you find volume and surface area of a rectangular prism? The formula of the surface area of rectangular prism is 2(wh + lw + lh)
Surface Area: Say that h is 2cm, w is 3cm and L, 5cm.
= 2 (6 + 15 + 10) = 2 x 31
Volume: 2 x 3 x 5 = 30cm^3 Finding the Surface Area and the volume of a cube Cube has all same heigh, length and width let's say that the length is 3cm. So height and width will also be 3 cm. First find the area of one side which is 3 x 3 = 9. And times it by 6 because there are 6 sides in in the cube. So it is 9 x 6 = 54cm^2. The Surface Area is 54cm^2. Finding the Volume and Surface Area of Cylinder Surface Area: Let's say that r= 2cm, h=3cm. The equation is 2 x π x r^2 + 2 x π x 2 x 3. It's (2 x 3.14 x 4) + (2 x 3.14 x 2 x 3) =
= 37.68 + 25.12
= 62.8cm^2 Volume: Let's say that r=2 and h=3. The equation is π x r^2 x h.
So it's 3.14 x 4 x 3 = 37.68cm^3 Finding the surface area and volume of Cone Surface Area: Let's say that r=2cm, s=3cm and h=5cm. The equation is π x r x s + π x r^2. It's 3.14 x 2 x 3 + 3.14 x 4 = 31.4cm^2 Volume: Let's say that r=2 and h=3. The equation is 1/3 x π x r^2 x h. Which is 1/3 x 3.14 x 4 x 3 = 12.56cm Volume: Cube has equal length of the sides so if the width is 3cm, height and length will also be 3cm. The equation to find the volume is L x W x H, so it's 3 x 3 x 3 which is 27cm^3 Surface Area and Volume of Sphere Surface Area: Let's say that r=2. The equation is 4 x π x r^2 which is 4 x 3.14 x 4. Then the answer is 50.24cm^2 Volume: Let's say that r=3. The equation to find the volume of Sphere is 4/3 x π x r^3. It is 4/3 x 3.14 x 27 = 113.04cm^3 So that was my presentation and that was the equations of finding the surface area and volume of a shape. Thank you for watching my Presentation My bibliography:
Peterson, Ivars. The Mathematical Tourist. New York: W.H. Freman and Company, 1988. Print. Big Question:
How do you find a surface area and volume of a shape? Essential questions:
What is a surface area and how do you find surface area of each shape?
What is volume and how do you find the volume of a shape?
How do you find the volume and surface area of cube, cylinder, rectangular prism, cone and sphere?