cube and cuboid
DESCRIPTION
CUBE and CUBOID. To calculate the sum of edges, length of face/plane diagonal, and diagonal, also area of diagonal plane. Created by Cep Andi Alim Subarkah for mathlabsky.wordpress.com. Created by Cep Andi Alim Subarkah for mathlabsky.wordpress.com. CUBE. H. G. F. - PowerPoint PPT PresentationTRANSCRIPT
CUBE and CUBOID
To calculate the sum of edges, length of face/plane diagonal, and diagonal, also area of diagonal plane
Created by Cep Andi Alim Subarkah for mathlabsky.wordpress.com Created by Cep Andi Alim Subarkah for mathlabsky.wordpress.com
CUBEThe sum of Edge
The length of face diagonal
The length of diagonal
The area of diagonal plane
12×𝑟
=
=
=
A B
C D
E
H
F
G
r cm
r cm
r cm
EXAMPLE 1
EXAMPLE 2
Face/Plane Diagonal
A B
CD
E
H
F
G
r cm
r cm
r cm
Look at ∆BAE, ∠A is right angle.
→→→→→
+
+
𝐵𝐸2=2×𝑟2
𝐵𝐸=√2×𝑟2𝐵𝐸=𝑟 √2
Diagonal
A B
CD
E
H
F
G
r cm
r cm
r cm
Look at ∆CAE, ∠A is right angle.
→→→→→
++
𝐶𝐸2=2𝑟 2+𝑟2=3𝑟2
𝐶𝐸=√3×𝑟2𝐶𝐸=𝑟 √3
Diagonal Plane
A B
C D
E
H
F
G
r cm
r cm
r cm
→→→
Look at rectangle ABGH
𝐴𝐵×𝐵𝐺
𝑟 ×𝑟 √2𝑟2√2
EXAMPLE 1Given a cube with measure of edge is 4 cm. calculatea. The sum of edges c. The length of diagonalb. The length of face diagonal d. The area of diagonal plane
The answer:
a. The sum of edges→12 x r = 12 x 4cm = 48 cm
b. The length of face diagonal→ r= 42 = = 32cm
c. The length of diagonal→ r= 43 = = 48cm
d. The area of diagonal plane→ = = cm2
EXAMPLE 2Given a cube with measure of face diagonal is cm. calculatea. The sum of edges c. The area of diagonal planeb. The length of diagonal
The answer:
L.O.F.D = r = r = : r = r = 6 cm
a. The sum of edges→12 x r = 12 x 6cm = 72 cm
b. The length of diagonal→ r= 63 = = 108cm
e. The area of diagonal plane→ = = cm2
CUBOID
A B
C D
E
H
F
G
l cmw cm
h cm
The sum of Edge
The length of face diagonal
The length of diagonal
4( 𝑙+𝑤+h)
√𝑙2+𝑤2+h2
√𝑙2+𝑤2
√𝑙2+h2√𝑤2+h2
Example 1Example 2
Face/Plane Diagonal
A B
C D
E
H
F
G
l cmw cm
h cm
Look at ∆CBF, ∠B is right angle.
Look at ∆ABC, ∠B is right angle.
𝐶𝐹=√𝑤2+h2
+
+
𝐴𝐶=√𝑙2+𝑤2
+
+
Diagonal
A B
C D
E
H
F
G
l cmw cm
h cmLook at ∆CAE, ∠A is right angle.
→→→→
++
𝐶𝐸2=𝑙2+𝑤2+h2
𝐶𝐸=√𝑙2+𝑤2+h2
EXAMPLE 1
Given a cuboid. Calculatea. The sum of edges
b. Face diagonal on basedc. The diagonal
The answer :
a. The sum of edges
: 4 (l + w + h): 4 (10 + 6 + 9): 4 (25): 100 cm
A B
CD
EF
GH
10 cm6 cm
9 cm
b. Length of : : : :
A B
CD
EF
GH
10 cm6 cm
9 cmc. The face diagonal on based
: : : :
d. The diagonal :
: : :
EXAMPLE 2
Sebuah balok memiliki ukuran rusuk alas 8 cm x 10cm. Jika panjang seluruh rusuk balok adalah 92cm, maka panjang diagonal ruang balok adalah …
Jawab
Panjang rusuk Seluruh = 92 4 (p + l + t) = 92 4 (8 + 10 + t) = 92 4 (18 + t) = 92 18 + t = 92 : 4 = 23 t = 23 – 18 = 5
Panjang diagonal ruang : :
: : : cm