math 10 chapter 1 - geometry of 3-d figures lesson 4 – calculating surface areas of 3-d shapes
TRANSCRIPT
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Math 10Chapter 1 - Geometry of 3-D Figures
Lesson 4 – Calculating Surface Areas of 3-D Shapes
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Todays Objectives: In this section we will:
Sketch a diagram to represent a problem that involves surface area (SA)
Determine the SA of a right cone, right prism, right pyramid, or sphere using an object or diagram
Determine an unknown dimension of a right cone, right prism, right pyramid, or sphere given the SA and remaining dimensions
Solve a problem that involves SA
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Surface Area Area is the two-dimensional (2-D) size of a
surface. Consider the area that your notebook is covering on the surface of your desk
Surface area (SA) of a solid is the total area of the exposed surfaces of a three-dimensional (3-D) object.
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Surface Area Consider a box. If you unfolded the sides,
top, bottom, front and back…how much area on your desk would it cover?
That would be the surface area of the box
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Review of areas
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Surface Area Formulas
h = height
r = radius
s = slant height
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Examples1. Height is 7 feet. Radius is 2 feet.
Label the cone and then solve the surface area.
Answer = 58 square feet
2. Lateral area is 220 square cms. Diameter is 10cm. What is the height of the cone?
Answer = 13.1 cm
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Surface Area Formulas Right Pyramid
Atriangle = 1/2bs Abase = b2
SA = 2bs + b2
Right pyramid is a 3D object with triangular faces and a polygon base
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Examples1. Slant height is 10 cm. Base length is 8cm.
Label the triangle and then solve the surface area.Answer = 224
square cm2. Slant height is 7.8 cm. Triangular base length is 9cm.
Label the triangle and then solve the surface area. Answer = 140.4
square cm
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Surface Area Formulas
Right Prism SA = 2(hl + lw + hw)
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Surface Area Formulas
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Example
Answer = 1508 square cm
Height is 8 cm. Diameter is 24cm.
Draw and label the cylinder and then solve the surface area.
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Surface Area Formulas
½ of sphere
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Examples
Diameter is 16cm.
Draw and label the sphere and then solve the surface area.
Answer = 804 square cm
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Combined Surface Areas Sometimes you may encounter 2 or more
shapes combined into one *Don’t forget that you may need to subtract and/or
add certain dimensions to find the correct answer Ex.) How can we find the SA of this shape?
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Answer!
51254 sq. in