holt geometry 10-4 surface area of prisms and cylinders 10-4 change in dimensions holt geometry
TRANSCRIPT
Holt Geometry
10-4 Surface Area of Prisms and Cylinders10-4 Change in dimensions
Holt Geometry
Holt Geometry
10-4 Surface Area of Prisms and Cylinders
Example 4: Exploring Effects of Changing Dimensions
The edge length of the cube is tripled. Describe the effect on the surface area.
Holt Geometry
10-4 Surface Area of Prisms and Cylinders
Example 4 Continued
original dimensions: edge length tripled:
Notice than 3456 = 9(384). If the length, width, and height are tripled, the surface area is multiplied by 32, or 9.
S = 6ℓ2
= 6(8)2 = 384 cm2
S = 6ℓ2
= 6(24)2 = 3456 cm2
24 cm
Holt Geometry
10-4 Surface Area of Prisms and Cylinders
Check It Out! Example 4
The height and diameter of the cylinder are
multiplied by . Describe the effect on the
surface area.
Holt Geometry
10-4 Surface Area of Prisms and Cylinders
original dimensions: height and diameter halved:
S = 2(112) + 2(11)(14)
= 550 cm2
S = 2(5.52) + 2(5.5)(7) = 137.5 cm2
11 cm
7 cm
Check It Out! Example 4 Continued
Notice than 550 = 4(137.5). If the dimensions are
halved, the surface area is multiplied by
Holt Geometry
10-4 Surface Area of Prisms and Cylinders
Example 3: Exploring Effects of Changing Dimensions
The base edge length and slant height of the regular hexagonal pyramid are both divided by
5. Describe the effect on the surface area.
Holt Geometry
10-4 Surface Area of Prisms and Cylinders
3 in.
2 in.
Example 3 Continued
original dimensions: base edge length and slant height divided by 5:
S = Pℓ + B 12 S = Pℓ + B
12
Holt Geometry
10-4 Surface Area of Prisms and Cylinders
Example 3 Continued
original dimensions: base edge length and slant height divided by 5:
3 in.
2 in.
Notice that . If the
base edge length and slant height are divided by 5,
the surface area is divided by 52, or 25.
Holt Geometry
10-4 Surface Area of Prisms and Cylinders
Check It Out! Example 3
The base edge length and slant height of the regular square pyramid are both multiplied
by . Describe the effect on the surface area.
Holt Geometry
10-4 Surface Area of Prisms and Cylinders
Check It Out! Example 3 Continued
original dimensions: multiplied by two-thirds:
By multiplying the dimensions by two-thirds, the surface area was multiplied by .
8 ft8 ft
10 ft
S = Pℓ + B 12
= 260 cm2
S = Pℓ + B 12
= 585 cm2