Jawaban:

Diameter = 20 cm dan Volume = 600 π cm³

Volume = π r² t

600 π = π (\frac{20}{2}

2

20

)² t

600 π = π 10² t

600 π = π 100 t

t = \displaystyle \frac{600\pi }{100\pi }

100π

600π

t = 6 cm

b. Jari-jari = 5 cm dan Luas permukaan = 120 π cm²

LP = 2 π r (r + t)

120 π = 2 π 5 (5 + t)

120 π = 10 π (5 + t)

5 + t = \displaystyle \frac{120\pi}{10\pi}

10π

120π

5 + t = 12

t = 12 - 5

t = 7 cm

c. V = 224 π cm³ dan d = 8 cm

Volume = π r² t

224 π = π 4² t

224 π = π 16 t

t = \displaystyle \frac{224\pi}{16\pi}

16π

224π

t = 14 cm

d. LP = 528 π cm² dan t = 13 cm

LP = 2 π r (r + t)

528π = 2 × π × r (r + 13) (sama coret π)

528 = 2 r (r + 13)

\displaystyle \frac{528}{2} = \frac{2 \times r (r + 13)}{2}

2

528

=

2

2×r(r+13)

264 = r² + 13r

r² + 13r - 264 = 0 (difaktorkan)

(r + 24) (r - 11) = 0

r + 24 = 0

r = -24 tidak memenuhi

atau

r - 11 = 0

r = 11 cm

jadi panjang jari-jari adalah 11 cm

e. LP = 450 π cm² dan t = 15 cm

LP = 2 π r (r + t)

450 π = 2 × π × r (r + 15) (sama coret π)

450 = 2 r (r + 15)

\displaystyle \frac{450}{2} = \frac{2 \times r (r + 15)}{2}

2

450

=

2

2×r(r+15)

225 = r² + 15r

r² + 15r - 225 = 0 (gunakan rumus abc)

r₁.r₂ = \displaystyle \frac{-15 \pm \sqrt{15^{2} + 4 (225) (1)}}{2(1)}

2(1)

−15±

15

2

+4(225)(1)

= \displaystyle \frac{-15 \pm \sqrt{225 + 900}}{2}

2

−15±

225+900

r = \displaystyle \frac{-15 + \sqrt{1125}}{2}

2

−15+

1125

= \displaystyle \frac{-15 + 33,54}{2}

2

−15+33,54

= \displaystyle \frac{18,54}{2}

2

18,54

= 9,27 cm

jadi panjang jari-jari adalah 9,27 cm

f. V = 294π cm³ dan t = 6 cm

V = π r² t

294π = π × r² × 6

294 = 6 r²

r² = \displaystyle \frac{294}{6}

6

294

r² = 49

r = 7 cm

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