Anonim A

01 April 2024 12:21

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Anonim A

01 April 2024 12:21

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Diketahui sebuah bola yang * dimasukkan ke dalam tabung, tepat berimpit dengan alas dan tutup tabung tersebut. Jika diameter bola adalah 14 cm dan tinggi tabung 30 cm, berapakah volume ruang di dalam tabung tapi di luar bola? Tolong bantu soal di atas kak.. (beserta caranya).

Diketahui sebuah bola yang * dimasukkan ke dalam tabung, tepat berimpit dengan alas dan tutup tabung tersebut. Jika diameter bola adalah 14 cm dan tinggi tabung 30 cm, berapakah volume ruang di dalam tabung tapi di luar bola?

 

Tolong bantu soal di atas kak.. (beserta caranya).

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Jawaban terverifikasi

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Community

Level 72

02 April 2024 01:52

Jawaban terverifikasi

<p>Soal ini ada yang salah, kalau bola berimpit dengan alas dan tutup tabung maka diameter bola = tinggi tabung. Artinya tinggi tabung sama dengan diameter bola, tetapi disini d = 14 cm, tinggi tabung = 30 cm. Jadi tidak nyambung....</p><p>&nbsp;</p><p>Saya akan bantu jawab dengan dua versi.</p><p><strong>Versi 1</strong> :&nbsp;</p><p>Bola berimpit dengan alas dan tutup tabung sehingga diameter bola = tinggi tabung.</p><p>&nbsp;</p><p>d = 14 cm</p><p>r = 14 /2 = 7 cm</p><p>t = 2r</p><p>𝞹 = 22/7</p><p>&nbsp;</p><p>Volume diluar bola = V. Tabung - V.Bola</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = (𝞹r<sup>2</sup>t) - (4/3 𝞹r<sup>3</sup>)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = (2𝞹r<sup>3</sup>) - (4/3 𝞹r<sup>3</sup>)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 𝞹r<sup>3</sup> (2 - 4/3)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 22/7 . 7<sup>3</sup> (6/3 - 4/3)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 22/7 . 343 (2/3)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 1.078 (2/3)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 718,67 cm<sup>3</sup></p><p>&nbsp;</p><p><strong>Versi 2 :&nbsp;</strong></p><p>diameter bola (d) = 14 cm&nbsp;</p><p>r = 7 cm</p><p>t = 30 cm</p><p>V. diluar bola = V. Tabung - V. bola</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = (𝞹r<sup>2</sup>t) - (4/3 𝞹r<sup>3</sup>)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 𝞹r<sup>2 </sup>(t - 4/3 r)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 22/7 .(7<sup>2</sup>) ( 30 - 4/3(7))</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 154 (30 - 28/3)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 154 (90/3 - 28/3)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 154 (62/3)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 3.182,67 cm<sup>3</sup></p>

Soal ini ada yang salah, kalau bola berimpit dengan alas dan tutup tabung maka diameter bola = tinggi tabung. Artinya tinggi tabung sama dengan diameter bola, tetapi disini d = 14 cm, tinggi tabung = 30 cm. Jadi tidak nyambung....

 

Saya akan bantu jawab dengan dua versi.

Versi 1

Bola berimpit dengan alas dan tutup tabung sehingga diameter bola = tinggi tabung.

 

d = 14 cm

r = 14 /2 = 7 cm

t = 2r

𝞹 = 22/7

 

Volume diluar bola = V. Tabung - V.Bola

                                        = (𝞹r2t) - (4/3 𝞹r3)

                                        = (2𝞹r3) - (4/3 𝞹r3)

                                        = 𝞹r3 (2 - 4/3)

                                        = 22/7 . 73 (6/3 - 4/3)

                                        = 22/7 . 343 (2/3)

                                        = 1.078 (2/3)

                                        = 718,67 cm3

 

Versi 2 : 

diameter bola (d) = 14 cm 

r = 7 cm

t = 30 cm

V. diluar bola = V. Tabung - V. bola

                            = (𝞹r2t) - (4/3 𝞹r3)

                            = 𝞹r2 (t - 4/3 r)

                            = 22/7 .(72) ( 30 - 4/3(7))

                            = 154 (30 - 28/3)

                            = 154 (90/3 - 28/3)

                            = 154 (62/3)

                            = 3.182,67 cm3


000000000000000000000000d5778fb25e86c7cf308d0234cdf9fadc3330197baa6d7346 0

Level 25

02 April 2024 02:01

Terimakasih kak, udah bantu jawab!

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Muhammad N

Level 43

17 Oktober 2024 12:44

<p>Hmmmm</p><p>&nbsp;</p>

Hmmmm

 


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