Lesson 31 Surface Area and Volume of Pyramids Homework WS 7.3

Lesson 31Surface Area and Volume of PyramidsHomework WS 7.3

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Surface Area and Volume - Pyramids

SA = ½lp + BSurface Area Formula:_________________________

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__________________

____________________________________

side

slant heightl

height

First thing to look for: _____________________________________the shape of the base

__________________________________square pyramid

(or altitude)

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Surface Area – Pyramid

1. Find the surface area of each regular pyramid with side length s, and slant height l. The number of sides of the base is given by n.

s = 6 l = 7 n = 4SA = ½lp + BSA = ½lp + lw

Square-lw

SA = ½(7)(24) + 36 SA = 84 + 36SA = 120


2. Find the surface area with side length s and slant height l, with the number of sides of the base given by n.

SA = ½lp + B

First thing to look for?: _____________________________________

s =8 L = 9 n = 3shape of the base

__________________triangle

SA = ½lp + ½bhSA = ½(9)(24) + ½(8)(43)SA = 135.7


The __________________of a solid is the total number of cubes that will exactly fill the interior.

volume

V = ⅓BhVolume Formula:_________________________

Where B is:________________________area of the base

3. V = ⅓Bh

4m

3m

7.6

Volume – PyramidFirst thing to look for: _____________________________________shape of the base

V = ⅓(12)(7.6)

V = 30.4 m³


4. A pentagonal pyramid with a base area of 24 square units and a volume of 104 cubic units. What is the height?

V = ⅓Bh104 = ⅓(24)h

104 = 8h13 = h

Surface Area and Volume - Pyramid

5. Find the volume of a square pyramid with the given dimensions.Base edge of 4, and a height equal to the diagonal of the base

4

442

V = ⅓Bh

V = ⅓(16)42

V = 30.2

Surface Area and Volume - Pyramid

6. A pyramid has a right triangle as its base, with leg lengths of 5 and 12. If the pyramids volume is 100, find its altitude.

V = ⅓Bh

5

12

100= ⅓(½(5)12)h100= ⅓(30)h100= 10h

10 = h


7. Find the surface area of a pyramid with the given dimensions.

n = 3, s = 14, l = 14First thing to look for: _____________________________________shape of the base

__________________triangleSA = ½lp + B

14

1414

7

73SA = ½(14)42 + ½(14)73SA = 294 + 84.9SA = 378.9

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Lesson 31 Surface Area and Volume of Pyramids Homework WS 7.3