10.6: Volumes of 10.6: Volumes of Pyramids and ConesPyramids and Cones

Objective: Objective:

To find the volume of To find the volume of pyramids and cones.pyramids and cones.

VolumeVolume: The space that a figure : The space that a figure occupies.occupies.

Volume of a Pyramid:

FORMULA:

H

V = 1/3 BH

Volume of a Cone:

FORMULA:

V = 1/3 BH or

V = 1/3 r²H

H

Example 1:Example 1:

Find the volume of a square pyramid Find the volume of a square pyramid with base edges 15 cm & height with base edges 15 cm & height 22cm.22cm.

V = 1/3 BH

= 1/3s2H

= 1/3 (15)2(22)

= 1650 cm³

Example 2:Example 2:

Find volume of a square pyramid Find volume of a square pyramid

with base edges 16 m and a with base edges 16 m and a

slant height 17 m:slant height 17 m:

What is missing?

How do we find it?

H

Pythagorean Theorem

Now, find volume

V = 1/3 BH

= 1/3bhH

= 1/3(16)(16)= 1/3(16)(16)(15)(15)

= 1280 m³= 1280 m³

Find HFind H

17² = 8² + H²17² = 8² + H²

289 = 64 + 289 = 64 + H²H²

225 = H²225 = H²

15 = H15 = H

H

Ex. #3 You try:Ex. #3 You try:

Find the volume of a square pyramid Find the volume of a square pyramid with base edges 24 m and slant with base edges 24 m and slant height 13 m:height 13 m:

V = 1/3 BH

= 1/3s2H

= 1/3(24)= 1/3(24)22(5)(5)

= 960 m³= 960 m³

Find H Find H

(5-12-(5-12-13)13)

5 = H5 = H

Example 4:Example 4:

Find the volume of the oblique cone:Find the volume of the oblique cone:

V = 1/3 r²H

= 1/3 = 1/3 (3²)(3²)(11)(11)

= 33= 33 in³ in³

Ex. 5 You try:Ex. 5 You try:Find the volume of each cone in terms Find the volume of each cone in terms

of of and also rounded as indicated: and also rounded as indicated:

a. To the nearest m3

V = 1/3 r²H

= 1/3 = 1/3 (6²)(6²)(12)(12)

= 144 = 144 m³ m³

≈ ≈ 452 m³452 m³

b. To the nearest mm3.

V = 1/3 r²H

= 1/3 = 1/3 (21²)(21²)(42)(42)

= 6174 = 6174 mm³ mm³

≈ ≈ 19396 mm³19396 mm³

Assignment:

Pg 554 #2-14 even,

15-18, 22-23, 28