11-3 Surface Areas of Pyramids and Cones

Quick Review

The lateral area of a regular pyramid is half the product of the perimeter of the base and the slant height. The lateral area of a right cone is half the product of the circumference of the base and the slant height. The surface area of each solid is the sum of the lateral area and the area of the base.

Example

What is the surface area of a cone with radius 3 in. and slant height 10 in.? Leave your answer in terms of π.

S . A .   = L . A . + B Use the formula for surface area of a cone.   = π r l + π r 2 Substitute formulas for lateral area and area of a circle.   = π ( 3 ) ( 10 ) + π ( 3 ) 2 Substitute  3  for  r  and  10  for  l .   = 30 π + 9 π Simplify.   = 39 π table with 5 rows and 4 columns , row1 column 1 , cap s . cap a . , column 2 equals , column 3 cap l . cap a . plus b , column 4 table with 2 rows and 1 column , row1 column 1 , cap use the formula for surface area of , row2 column 1 , a cone. , end table , row2 column 1 , , column 2 equals , column 3 pi , r l plus , pi , r squared , column 4 table with 2 rows and 1 column , row1 column 1 , cap substitute formulas for lateral area , row2 column 1 , and area of a circle. , end table , row3 column 1 , , column 2 equals , column 3 pi open 3 close open 10 close plus pi . open 3 , close squared , column 4 cap substitute . 3 , for , r , and , 10 , for , l . , row4 column 1 , , column 2 equals , column 3 30 pi , plus 9 , pi , column 4 cap simplify. , row5 column 1 , , column 2 equals , column 3 39 pi , end table

The surface area of the cone is 39 π  in . 2 . 39 pi . in , . squared , .

Exercises

Find the surface area of each figure. Round your answers to the nearest tenth.

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20. Find the formula for the base area of a prism in terms of surface area and lateral area.

11-4 and 11-5 Volumes of Prisms, Cylinders, Pyramids, and Cones

Quick Review

The volume of a space figure is the space that the figure occupies. Volume is measured in cubic units. The volume of a prism and the volume of a cylinder are the product of the area of a base and the height of the solid. The volume of a pyramid and the volume of a cone are one third the product of the area of the base and the height of the solid.

Example

What is the volume of a rectangular prism with base 3 cm by 4 cm and height 8 cm?

V = B h Use the formula for the volume of a prism.   = ( 3 · 4 ) ( 8 ) Substitute.   = 96 Simplify. table with 3 rows and 4 columns , row1 column 1 , v , column 2 equals , column 3 b h , column 4 cap use the formula for the volume of a prism. , row2 column 1 , , column 2 equals , column 3 open 3 middle dot 4 , close open 8 close , column 4 cap substitute. , row3 column 1 , , column 2 equals , column 3 96 , column 4 cap simplify. , end table

The volume of the prism is 96  cm 3 . 96 . cm cubed , .

Exercises

Find the volume of each figure. If necessary, round to the nearest tenth.

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