How To Find The Surface Area Of A Composite Figure
A blended 3D effigy is a 3 dimensional effigy made up of basic three dimensional figures such as cubes, prisms, pyramids, cylinders, cones, etc.
To find the surface surface area of a blended 3D effigy, add the areas of each geometric figure making upwards the composite 3D figure.
To find the volume of a composite 3D effigy, draw whatsoever necessary planes to view the figure every bit basic iii dimensional figures, then:
- add bones figure volumes belonging to the composite shape
- decrease basic figure volumes NOT belonging to the composite figure
Problem
Observe the surface expanse and volume of the composite 3D effigy below.
View the composite 3D figure equally a right rectangular prism together with a cube, then find any missing lengths in order to calculate the surface surface area and volume.
SURFACE Surface area SOLUTION
Notation that in that location are more elegant solutions to calculate the surface expanse than the one shown below, but the solution shown below illustrates separating a blended 3D figure into basic 3D figures.
S: Surface surface area of composite 3D effigy.
A: Area.
Due south = AForepart + ABACK + ALEFT + ARIGHT + ATiptop + ABOTTOM
S = [(15 cm)(5 cm) + (v cm)(5 cm)] + (xx cm)(v cm) + (x cm)(5 cm) + [(five cm)(5 cm) + (5 cm)(5 cm)] + [(15 cm)(10 cm) + (v cm)(five cm)] + [(15 cm)(10 cm) + (v cm)(5 cm)]
Due south = 650 cm2
The surface area of the given composite 3D figure is 650 cm2
VOLUME SOLUTION ONE
V: Volume.
Vcomposite 3D figure = 5rectangular right prism + Fivecube
Vcomposite 3D effigy = (15 cm)(10 cm)(5 cm) + (five cm)3
Fiveblended 3D effigy = 750 cmthree + 125 cm3
5composite 3D effigy = 875 cm3
The volume of the given composite 3D figure is 875 cm3
AREA SOLUTION TWO
Note that there are other similar ways to summate the volume of the given composite 3D figure. For example rather than viewing the composite 3D effigy as a rectangular correct prsim together with a cube, it can be viewed as rectangular right prism less a cube.
5: Volume.
Vcomposite 3D figure = Vrectangular right prism - Vcube
Vblended 3D effigy = (20 cm)(10 cm)(5 cm) - (five cm)3
Vcomposite 3D figure = chiliad cm3 - 125 cm3
5composite 3D figure = 875 cm3
The book of the given composite 3D figure is 875 cm3
Source: https://www.learnalberta.ca/content/memg/division03/composite%203d%20figure/index.html
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