Exercise Zone : Bangun Ruang Sisi Lengkung
Table of Contents
Tipe:
No.
Sebuah bola dimasukkan ke dalam tabung, diameter bola sama dengan diameter tabung = 3,5 cm, tinggi tabung di luar bola adalah 10 cm, maka volume tabung di luar bola adalah....205\dfrac13 cm3250\dfrac23 cm3225\dfrac25 cm3
225\dfrac35 cm3204\dfrac13 cm3
ALTERNATIF PENYELESAIAN
r = 3,5 = \dfrac72
Volume tabung: \begin{aligned} V_t&=\pi r^2t\\ &=\dfrac{\cancelto{\color{blue}11}{22}}{\cancel{7}}\cdot\dfrac{\cancel{7}}{\cancel{2}}\cdot\dfrac7{\cancel{2}}\cdot\cancelto{\color{blue}5}{10}\\ &=385 \end{aligned} Volume bola: \begin{aligned} V_b&=\dfrac43\pi r^3\\ &=\dfrac{\cancel{4}}3\cdot\dfrac{\cancelto{\color{blue}11}{22}}{\cancel{7}}\cdot\dfrac{\cancel{7}}{\cancel{2}}\cdot\dfrac{7}{\cancel{2}}\cdot\dfrac{7}{\cancel{2}}\\ &=\dfrac{539}3\\ &=179\dfrac23 \end{aligned} Volume tabung di luar bola: \begin{aligned} V&=V_t-V_b\\ &=385-179\dfrac23\\ &=206-\dfrac23\\ &=\boxed{\boxed{205\dfrac13}} \end{aligned}
Volume tabung: \begin{aligned} V_t&=\pi r^2t\\ &=\dfrac{\cancelto{\color{blue}11}{22}}{\cancel{7}}\cdot\dfrac{\cancel{7}}{\cancel{2}}\cdot\dfrac7{\cancel{2}}\cdot\cancelto{\color{blue}5}{10}\\ &=385 \end{aligned} Volume bola: \begin{aligned} V_b&=\dfrac43\pi r^3\\ &=\dfrac{\cancel{4}}3\cdot\dfrac{\cancelto{\color{blue}11}{22}}{\cancel{7}}\cdot\dfrac{\cancel{7}}{\cancel{2}}\cdot\dfrac{7}{\cancel{2}}\cdot\dfrac{7}{\cancel{2}}\\ &=\dfrac{539}3\\ &=179\dfrac23 \end{aligned} Volume tabung di luar bola: \begin{aligned} V&=V_t-V_b\\ &=385-179\dfrac23\\ &=206-\dfrac23\\ &=\boxed{\boxed{205\dfrac13}} \end{aligned}
Jadi, volume tabung di luar bola adalah 205\dfrac13 cm3.
JAWAB: A
JAWAB: A
No.
Tinggi dan jari-jari suatu kerucut sama dengan jari-jari sebuah bola. Jika panjang garis pelukis kerucut 26 cm, panjang diameter bola adalah .... cm- 13
13\sqrt2
- 26
26\sqrt2
ALTERNATIF PENYELESAIAN
t = r
s = 26 \begin{aligned}r^2+t^2&=s^2\\r^2+r^2&=26^2\\2r^2&=676\\r^2&=\dfrac{676}2\\&=338\\r&=\sqrt{338}\\&=13\sqrt2\end{aligned}
s = 26 \begin{aligned}r^2+t^2&=s^2\\r^2+r^2&=26^2\\2r^2&=676\\r^2&=\dfrac{676}2\\&=338\\r&=\sqrt{338}\\&=13\sqrt2\end{aligned}
\begin{aligned}d&=2r\\&=2\cdot13\sqrt2\\&=\boxed{\boxed{26\sqrt2}}\end{aligned}
Jadi, panjang diameter bola adalah 26\sqrt2 cm.
JAWAB: D
JAWAB: D
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