This document provides solutions to calculating the volume and total surface area of various solids and rotational bodies. It includes: 1) Calculating the volume and total surface area for solids with given heights and radii. 2) Calculating the volume and total surface area for rotational bodies with given radii and heights rotated around given axes. 3) The solutions provide the calculated volumes and total surface areas for each problem.

1. MaTeX2º ESO
16.1. Volumen y Superficie
1. Hallar el volumen y la superficie total de los cuerpos.
h
8
(a) h = 10
8
a
h
(b) h = 10 , a = 5,5
a
h
9
(c) h = 12 , a = 8
h
9 a
(d) h = 10 , a = 8
h
8
a
(e) h = 10 , a = 5,5
h
5
a
(f) h = 10 , a = 6
5
4
3
2
(g)
h
8
4
(h) h = 6
Soluciones
1. a) V = 213,22; AT ≈ 236,33. b) V = 266,67; AT ≈ 338,25. c) V = 864; AT ≈ 605,4. d) V = 2160; AT = 972. e)
V = 1100; AT = 620. f ) V = 1200; AT = 640. g) V = 42; AT = 76. h) V = 224; AT = 80 + 24
√
40.
MaTEX-2-ESO 8 Matem´aticas

2. MaTeX2º ESO
16.2. Cuerpos de revoluci´on
1. Hallar el volumnen y la superficie total de los cuerpos.
3
(a)
4
5
(b)
h
5
(c) h = 6
4
4
(d)
4
5
(e)
4
4
4
(f)
8
4
10
(g)
4
6
5
(h)
8
5
2
1
(i)
Soluciones
1. a) V = 36π; AT = 36π. b) V = 80π; AT = 72π. c) V = 50π; AT = 64,05π. d) V =
320
3
π; AT = 80π. e) V =
208
3
π; AT =
(32 + 4
√
41)π. f ) V =
256
3
π; AT = (48 + 16
√
2)π. g) V =
1120
3
π; AT = (80 + 12
√
116)π. h) V = 168π; AT = 132π. i)
V = 44π; AT = 100π.
MaTEX-2-ESO 9 Matem´aticas