Question

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Answer 1

Jawaban:

Penyelesaian :

Luas permukaan kubus adalah 294 cm². Hitunglah

• a. Panjang diagonal bidangnya
• b. Panjang diagonal ruangnya
• c. Volume kubus

Cari dulu panjang rusuk kubus

[tex] \sf Luas = 6 \times {r}^{2} \: \\ \sf 294 = 6 \times {r}^{2} \\ \sf {r}^{2} = \frac{294}{6} \: \\ \sf {r}^{2} = 49 \: \: \: \: \: \\ \sf r = \sqrt{49} \\ \sf r = \red{7 \: cm}[/tex]

[tex] \boxed{ \pink{ \sf a. \: panjang \: diagonal \: bidang }} \\ \sf diagonal = \sqrt{ {r}^{2} + {r}^{2} } \: \: \: \\ \sf diagonal = \sqrt{ {7}^{2} + {7}^{2} } \: \: \\ \sf diagonal = \sqrt{49 + 49} \: \: \\ \sf diagonal = \sqrt{98} \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf diagonal = \sqrt{49 \times 2} \: \: \: \: \\ \sf diagonal = \sqrt{49} \times \sqrt{2} \\ \sf diagonal = \red{7 \sqrt{2} \: cm \: \: \: \: \: }[/tex]

[tex] \boxed{ \purple{ \sf b. \: panjang \: diagonal \: ruang}} \\ \sf diagonal = \sqrt{ {r}^{2} + {r}^{2} + {r}^{2} } \: \: \: \\ \sf diagonal = \sqrt{ {7}^{2} + {7}^{2} + {7}^{2} } \: \\ \sf diagonal = \sqrt{49 + 49 + 49} \\ \sf diagonal = \sqrt{147} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf diagonal = \sqrt{49 \times 3} \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf diagonal = \sqrt{49} \times \sqrt{3} \: \: \: \: \: \: \: \: \\ \sf diagonal = \red{7 \sqrt{3} \: cm} \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex] \boxed{ \blue{ \sf c. \: volume \: kubus}} \\ \sf v = r \times r \times r \: \: \: \: \: \: \: \\ \sf v = 7 \times 7 \times 7 \: \: \: \: \: \\ \sf v = 7 \times 49 \: \: \: \: \: \: \: \: \: \: \\ \sf v = \red{343 \: {cm}^{3} } \: \: \: \: \: \: \: [/tex]

'비상'

Answer 2

Penjelasan dengan langkah-langkah:

cari sisi dulu

s = √luas 6 sisi ÷ 6sisi

s = √294 ÷ 6

s = √49

s = 7 cm

diagonal bidang (sisi miring dalam segitiga siku²)

= √7²+7²

= √49 + 49

= √98

= √7² × 2

= 7√2

diagoanal ruang

= 7√2 + 7²

= √98 + 49

= √147

= √7²×3

= 7√3

V = Lsisi × t

V = (7 × 7) × 7

V = 49 × 7

V = 343 cm³