Unit 10
Akal Pintar
Pak Hamid memotong sebongkah kayu berbentuk kuboid. Luas permukaan berwarna kuning ialah 20 cm². Panjang sisi ke belakang ialah 6 cm.Berapakah isi padu bongkah kayu itu?
已知一个面的面积求体积 = cari isi padu daripada luas satu permukaan
题目没有给出长、宽、高三个数字，只给了一个面的面积和另外一条边。想一想：一个面的面积已经是两条边相乘的结果，还差哪一条边？只要找对那条边，就能算出体积。
例子：一个面是 10 cm²，和它垂直的边长 3 cm，体积 = 30 cm³。
注意：不知道每一条边的长度，也有办法算体积。
volume from the area of one face = cari isi padu daripada luas satu permukaan
The question does not give all three measurements; it gives the area of one face and one more edge. Think: the area of a face is already two edges multiplied together, so which edge is still missing? Find the right edge and you can work out the volume.
Example: a face of 10 cm² and an edge of 3 cm at right angles to it give a volume of 30 cm³.
Watch out: you can find the volume without knowing every edge length.
Cara
Luas permukaan × sisi yang serenjang
Isi padu = 20 cm² × 6 cm = 120 cm³
面积乘垂直的边 = luas permukaan × sisi yang serenjang
长方体的体积 = 底面积 × 高。其实任何一个面都可以当成“底”，只要乘上和这个面垂直的那条边就行。黄色的面是二十平方厘米，往后伸的边六厘米和黄色面垂直，所以体积 = 二十乘六，等于一百二十立方厘米。
例子：前面的面积 14 m²，往后的边 5 m，体积 = 70 m³。
注意：要乘的是不在那个面上的边。
face area × the perpendicular edge = luas permukaan × sisi yang serenjang
The volume of a cuboid is base area × height, and any face can act as the base, as long as you multiply by the edge at right angles to that face. The yellow face is 20 cm² and the 6 cm edge going back is perpendicular to it, so the volume is 20 × 6 = 120 cm³.
Example: a front face of 14 m² and an edge of 5 m going back give 70 m³.
Watch out: multiply by the edge that is not part of that face.
Mengapa?
Lapisan ke belakang
1 lapisan = 20 kiub
6 lapisan = 20 × 6 = 120 kiub = 120 cm³
6 lapisan = 20 × 6 = 120 kiub = 120 cm³
为什么这样算 = mengapa cara ini betul
把木块切成边长一厘米的小正方体。黄色的面有二十平方厘米，表示紧贴着黄色面的那一层有二十个小正方体。往后一共有六层，每层都一样，所以一共有二十乘六，一百二十个小正方体，也就是一百二十立方厘米。
例子：一层 9 个小正方体、往后 4 层，一共 36 个，体积 36 cm³。
注意：每一层的个数等于那个面的面积数字。
why it works = mengapa cara ini betul
Imagine cutting the block into 1 cm cubes. The yellow face is 20 cm², so the layer touching the yellow face holds 20 cubes. There are six identical layers going back, so there are 20 × 6 = 120 cubes, which is 120 cm³.
Example: 4 layers of 9 cubes make 36 cubes, a volume of 36 cm³.
Watch out: the number of cubes in a layer equals the area number of that face.
Semak
Semak dengan panjang × lebar × tinggi
5 cm × 4 cm = 20 cm² ✓
5 cm × 4 cm × 6 cm = 120 cm³ ✓
5 cm × 4 cm × 6 cm = 120 cm³ ✓
用长宽高验算 = semak dengan panjang × lebar × tinggi
假如黄色面的两条边是五厘米和四厘米，五乘四正好二十平方厘米，和题目给的一样。再用长乘宽乘高：五乘四乘六，也是一百二十立方厘米。两种方法答案相同，说明“面积乘垂直的边”是对的。
例子：面 3 cm × 2 cm = 6 cm²，往后 7 cm：6 × 7 = 42，3 × 2 × 7 = 42。
注意：题目只给面积时，不需要猜两条边各是多少。
checking with length × width × height = semak dengan panjang × lebar × tinggi
Suppose the yellow face is 5 cm by 4 cm: 5 × 4 = 20 cm², just as given. Length × width × height is 5 × 4 × 6 = 120 cm³ as well. Both ways agree, so face area × perpendicular edge is right.
Example: a 3 cm × 2 cm face is 6 cm²; with 7 cm going back, 6 × 7 = 42 and 3 × 2 × 7 = 42.
Watch out: when only the area is given, there is no need to guess the two edges.
Cuba
Permukaan yang berlorek mempunyai luas 27 m². Tentukan isi padu bongkah ini.
涂色面乘另一边 = luas berlorek × sisi
涂色的面积已经是两条边的乘积，只要再乘上和它垂直、往后伸的那条边；平方米乘米，单位是立方米。
例子：涂色面 16 m²，往后 3 m，体积 = 48 m³。
注意：面积和边相加没有意义；体积的单位要写 m³。
shaded face × the other edge = luas berlorek × sisi
The shaded area is already two edges multiplied, so multiply it by the edge at right angles to it, going back. Square metres times metres give cubic metres.
Example: a shaded face of 16 m² with 3 m going back gives 48 m³.
Watch out: adding an area and an edge makes no sense, and the volume unit must be m³.
Cuba
Isi padu kuboid ini ialah 132 cm³. Berapakah panjang sisi x?
反过来求边长 = cari panjang sisi
体积 = 涂色面面积 × 往后的边。现在知道体积和面积，就想：面积乘几等于体积？用除法：体积 ÷ 面积，得到的是一条边的长度，单位用厘米。
例子：体积 90 cm³、涂色面 18 cm²，边长 = 90 ÷ 18 = 5 cm。
注意：体积减面积或加面积都不是方法。
finding the edge = cari panjang sisi
Volume = shaded face area × the edge going back. You know the volume and the area, so ask: the area times what gives the volume? Divide: volume ÷ area gives the length of an edge in centimetres.
Example: volume 90 cm³ and shaded face 18 cm² give an edge of 90 ÷ 18 = 5 cm.
Watch out: subtracting or adding the area and the volume is not the method.
Cuba
Luas permukaan berlorek ialah 35 cm². Cari isi padu bongkah ini.
选对要乘的边 = pilih sisi yang betul
图上标了两条边。其中一条就在涂色的面上，它已经算在面积里了；另一条往后伸、和涂色面垂直。体积 = 涂色面面积 × 垂直的那条边。
例子：涂色面 12 cm²、面上的边 4 cm、往后的边 9 cm，体积 = 12 × 9 = 108 cm³。
注意：乘上已经在面上的边，等于同一条边算了两次。
choosing the right edge = pilih sisi yang betul
Two edges are labelled. One lies on the shaded face, so it is already inside the area; the other goes back, at right angles to the shaded face. Volume = shaded area × the perpendicular edge.
Example: a shaded face of 12 cm² with a 4 cm edge on it and a 9 cm edge going back gives 12 × 9 = 108 cm³.
Watch out: multiplying by the edge on the face counts that edge twice.
Ringkasan
Syabas!
Isi padu = luas permukaan × sisi serenjang
Darab luas satu permukaan dengan sisi yang berserenjang dengan permukaan itu.
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