\(\color{blue}\textbf{Volume} = \dfrac{1}{3}\times \pi \text{r}^2 \times \text{t}\)
Sebuah kerucut memiliki jari-jari alas sepanjang 14 cm dan tinggi 42 cm. Tentukan volume kerucut tersebut!
\(\text{Volume kerucut} = \dfrac{1}{3}\times \pi \text{r}^2 \times \text{t}\)
\(\text{Volume kerucut} = \dfrac{1}{3}\cdot \dfrac{22}{7}\cdot 14^2 \cdot 42\)
\(\text{Volume kerucut} = \dfrac{1}{\cancel{3}}\cdot \dfrac{22}{\cancel{7}}\cdot \cancelto{2}{14} \cdot 14 \cdot \cancelto{14}{42}\)
\(\text{Volume kerucut} = 22\cdot 2\cdot 14 \cdot 14\)
\(\text{Volume kerucut} = 8.624 \text{ cm}^3\)
Tentukan volume kerucut yang memiliki diameter alas 21 cm dan tinggi 24 cm.
Jari-jari = \(\dfrac{1}{2}\) × diameter
Jari-jari = \(\dfrac{1}{2}\) × 21 = \(\dfrac{21}{2} \text{ cm}\)
\(\text{Volume kerucut} = \dfrac{1}{3}\times \pi \text{r}^2 \times \text{t}\)
\(\text{Volume kerucut} = \dfrac{1}{3}\cdot \dfrac{22}{7}\cdot \dfrac{21}{2} \cdot \dfrac{21}{2} \cdot 24\)
\(\text{Volume kerucut} = \dfrac{1}{\cancel{3}}\cdot \dfrac{22}{\cancel{7}}\cdot \dfrac{\cancel{21}}{\cancel{2}} \cdot \dfrac{21}{\cancel{2}} \cdot \cancelto{6}{24}\)
\(\text{Volume kerucut} = 22\cdot 21 \cdot 6\)
\(\text{Volume kerucut} = 2.772 \text{ cm}^3\)
Sebuah kerucut memiliki luas alas 54 cm² dan volume 216 cm³. Tentukan tinggi kerucut tersebut.
\(\text{Volume} = \dfrac{1}{3}\times \text{luas alas} \times \text{tinggi}\)
\(216 \text{ cm}^3 = \dfrac{1}{3}\times 54 \text{ cm}^2 \times \text{tinggi}\)
\(216 \text{ cm}^3 = \dfrac{1}{\cancel{3}}\times \cancelto{18}{54} \text{ cm}^2 \times \text{tinggi}\)
\(\text{Tinggi kerucut} = 216 \div 18\)
\(\text{Tinggi kerucut} = 12 \text{ cm}\)
jadi, tinggi kerucut tersebut adalah 12 cm
Sebuah kerucut memiliki diameter alas 14 cm dan volume 1.694 cm³. Tentukan tinggi kerucut tersebut.
Jari-jari = \(\dfrac{1}{2}\) × diameter
Jari-jari = \(\dfrac{1}{2}\) × 14 = 7 cm
\(\text{Volume kerucut} = \dfrac{1}{3}\times \pi \text{r}^2 \times \text{t}\)
\(1.694 = \dfrac{1}{3}\cdot \dfrac{22}{\cancel{7}}\cdot \cancel{7} \cdot 7 \cdot \text{t}\)
\(1.694 = \dfrac{1}{3}\cdot 22 \cdot 7 \cdot \text{t}\)
Kalikan kedua ruas dengan 3,
\(\color{blue} 3 \times \color{black} 1.694 = \color{blue} \cancel{3} \times \color{black} \dfrac{1}{\cancel{3}}\cdot 22 \cdot 7 \cdot \text{t}\)
\(5.082 = 154 \cdot \text{t}\)
\(\text{t} = 5.082 \div 154\)
\(\text{t} = 33 \text{ cm}\)
jadi, tinggi kerucut tersebut adalah 33 cm
Sebuah kerucut memiliki tinggi 27 cm dan volume 22.176 cm³. Tentukan panjang jari-jari alas kerucut tersebut.
\(\text{Volume kerucut} = \dfrac{1}{3}\times \pi \text{r}^2 \times \text{t}\)
\(22.176 = \dfrac{1}{3} \cdot \dfrac{22}{7} \cdot \text{r}^2 \cdot 27\)
\(22.176 = \dfrac{1}{\cancel{3}} \cdot \dfrac{22}{7} \cdot \text{r}^2 \cdot \cancelto{9}{27}\)
\(22.176 = \dfrac{198}{7} \cdot \text{r}^2\)
Kalikan kedua ruas dengan 7,
\(\color{blue} 7 \times \color{black} 22.176 = \color{blue} \cancel{7} \times \color{black}\dfrac{198}{\cancel{7}} \cdot \text{r}^2\)
\(155.232 = 198 \cdot \text{r}^2\)
\(\text{r}^2 = 155.232 \div 198\)
\(\text{r}^2 = 784\)
\(\text{r} = \sqrt{784}\)
\(\text{r} = 28 \text{ cm}\)
jadi, jari-jari kerucut tersebut adalah 28 cm
