Kategori: Kerucut

Jawaban: C

Jari-jari alas kerucut = \(\dfrac{1}{2}\) × 48 cm = 24 cm

Tinggi kerucut = 2 × 48 cm = 96 cm

Karena \(\dfrac{1}{4}\) bagian nasi tumpeng dimakan, maka nasi tumpeng yang tersisa tinggal \(1\:-\:\dfrac{1}{4} = \dfrac{3}{4}\) bagian.

Volume nasi tumpeng yang tersisa dapat dihitung sebagai berikut:

\(\text{Volume sisa } = \dfrac{3}{4}\times \text{ volume kerucut}\)

\(\text{Volume sisa } = \dfrac{3}{4}\times \dfrac{1}{3}\times \pi \text{r}^2 \times \text{t}\)

\(\text{Volume sisa } = \dfrac{\cancel{3}}{4}\cdot \dfrac{1}{\cancel{3}}\cdot 3,14 \cdot  24 \cdot 24  \cdot 96\)

\(\text{Volume sisa } = \dfrac{1}{\cancel{4}}\cdot 3,14 \cdot  \cancelto{6}{24} \cdot 24  \cdot 96\)

\(\text{Volume sisa } = 3,14 \cdot  13.824\)

\(\text{Volume sisa } = 43.407,36 \text{ cm}^3\)

Jawaban: C

Jari-jari kerucut (r) = \(\dfrac{1}{2}\) × 30 cm = 15 cm

Panjang garis pelukis (s) = 17 cm

Topi ulang tahun yang dibut Joni berbentuk kerucut tanpa alas, sehingga luas kertas karton yang dibutuhkan untuk membuat sebuah topi sama dengan luas selimut kerucut.

\(\text{Luas selimut} = \pi \text{r} \text{s}\)

\(\text{Luas selimut} = 3,14 \cdot 15 \cdot 17\)

\(\text{Luas selimut} = 3,14 \cdot 255\)

\(\text{Luas selimut} = 800,7 \text{ cm}^2\)

Jadi, luas karton yang dibutuhkan Joni adalah 800,7 cm²

Panjang garis pelukis (s) = 17 cm

Jari-jari alas (r) = 8 cm

\(\text{Luas permukaan kerucut} = \pi \text{r}(\text{r} + \text{s})\)

\(\text{Luas permukaan kerucut} = 3,14\cdot 8 (8 + 17)\)

\(\text{Luas permukaan kerucut} = 3,14\cdot 8 (25)\)

\(\text{Luas permukaan kerucut} = 3,14\cdot 200\)

\(\text{Luas permukaan kerucut} = 628 \text{ cm}^2\)

Panjang garis pelukis (s) = 25 cm

Jari-jari alas (r) = 14 ÷ 2 = 7 cm

\(\text{Luas permukaan kerucut} = \pi \text{r}(\text{r} + \text{s})\)

\(\text{Luas permukaan kerucut} = \dfrac{22}{7}\cdot 7 (7 + 25)\)

\(\text{Luas permukaan kerucut} = \dfrac{22}{\cancel{7}}\cdot \cancel{7} (32)\)

\(\text{Luas permukaan kerucut} = 704 \text{ cm}^2\)

\(\text{Volume kerucut} = \dfrac{1}{3}\times \pi \text{r}^2 \times \text{t}\)

\(\text{Volume kerucut} = \dfrac{1}{3}\cdot \dfrac{22}{7}\cdot 14^2 \cdot 42\)

\(\text{Volume kerucut} = \dfrac{1}{\cancel{3}}\cdot \dfrac{22}{\cancel{7}}\cdot \cancelto{2}{14} \cdot 14 \cdot \cancelto{14}{42}\)

\(\text{Volume kerucut} = 22\cdot 2\cdot 14 \cdot 14\)

\(\text{Volume kerucut} = 8.624 \text{ cm}^3\)

Jari-jari = \(\dfrac{1}{2}\) × diameter

Jari-jari = \(\dfrac{1}{2}\) × 21 = \(\dfrac{21}{2} \text{ cm}\)

\(\text{Volume kerucut} = \dfrac{1}{3}\times \pi \text{r}^2 \times \text{t}\)

\(\text{Volume kerucut} = \dfrac{1}{3}\cdot \dfrac{22}{7}\cdot \dfrac{21}{2} \cdot \dfrac{21}{2} \cdot 24\)

\(\text{Volume kerucut} = \dfrac{1}{\cancel{3}}\cdot \dfrac{22}{\cancel{7}}\cdot \dfrac{\cancel{21}}{\cancel{2}} \cdot \dfrac{21}{\cancel{2}} \cdot \cancelto{6}{24}\)

\(\text{Volume kerucut} = 22\cdot 21 \cdot 6\)

\(\text{Volume kerucut} = 2.772 \text{ cm}^3\)

\(\text{Volume} = \dfrac{1}{3}\times \text{luas alas} \times \text{tinggi}\)

\(216 \text{ cm}^3 = \dfrac{1}{3}\times 54 \text{ cm}^2 \times \text{tinggi}\)

\(216 \text{ cm}^3 = \dfrac{1}{\cancel{3}}\times \cancelto{18}{54} \text{ cm}^2 \times \text{tinggi}\)

\(\text{Tinggi kerucut} = 216 \div 18\)

\(\text{Tinggi kerucut} = 12 \text{ cm}\)

jadi, tinggi kerucut tersebut adalah 12 cm

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

\(\text{Volume kerucut} = \dfrac{1}{3}\times \pi \text{r}^2 \times \text{t}\)

\(22.176 = \dfrac{1}{3} \cdot \dfrac{22}{7} \cdot \text{r}^2 \cdot 27\)

\(22.176 = \dfrac{1}{\cancel{3}} \cdot \dfrac{22}{7} \cdot \text{r}^2 \cdot \cancelto{9}{27}\)

\(22.176 = \dfrac{198}{7} \cdot \text{r}^2\)

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