گام به گام کاردرکلاس صفحه 74 درس 6 ریاضی هفتم (سطح و حجم)

رابطه حجم منشور:

\(V = S \times h\)

\(\left\{ \begin{array}{l}S = 3\\\\h = 4\end{array} \right. \Rightarrow V = 3 \times 4 = 12\)

\(\left\{ \begin{array}{l}S = 4/5\\\\h = 2\end{array} \right. \Rightarrow V = 4/5 \times 2 = 9\)

\(\left\{ \begin{array}{l}S = 2/5\\\\h = 4\end{array} \right. \Rightarrow V = 2/5 \times 4 = 10\)

\(\left\{ \begin{array}{l}S = 4/5\\\\h = 2/5\end{array} \right. \Rightarrow V = 4/5 \times 2/5 = 11/25\)

\(\left\{ \begin{array}{l}S = 3\\\\h = 5\end{array} \right. \Rightarrow V = 3 \times 5 = 15\)

\(\left\{ \begin{array}{l}S = 6/5\\\\h = 1/5\end{array} \right. \Rightarrow V = 6/5 \times 1/5 = 9/75\)

\(\left\{ \begin{array}{l}S = 3\\\\h = 5/5\end{array} \right. \Rightarrow V = 3 \times 5/5 = 16/5\)

\(\left\{ \begin{array}{l}S = 4/6\\\\h = 6/2\end{array} \right. \Rightarrow V = 4/6 \times 6/2 = 28/52\)

\(\left\{ \begin{array}{l}S = 3\\\\h = 25\end{array} \right. \Rightarrow V = 3 \times 25 = 75\)

\(\left\{ \begin{array}{l}S = 7/5\\\\h = 12\end{array} \right. \Rightarrow V = 7/5 \times 12 = 90\)

\(\left\{ \begin{array}{l}S = 6 \times 5 = 30\\\\h = 3\end{array} \right. \Rightarrow V = 30 \times 3 = 90\)

\(\left\{ \begin{array}{l}S = 5 \times 5 = 25\\\\h = 5\end{array} \right. \Rightarrow V = 25 \times 5 = 125\)

\(\begin{array}{l}\left\{ \begin{array}{l}S = 4 \times 4 \times 3/14 = 50/24\\\\h = 7\end{array} \right.\\\\ \Rightarrow V = 50/24 \times 7 = 351/68\end{array}\)

\(\begin{array}{l}\left\{ \begin{array}{l}S = \frac{{(3 + 8) \times 3}}{2} = \frac{{33}}{2}\\\\h = 6\end{array} \right.\\\\ \Rightarrow V = \frac{{33}}{2} \times 6 = 33 \times 3 = 99\end{array}\)

\(\begin{array}{l}\left\{ \begin{array}{l}S = (2 \times 3) - (1 \times 1) = 6 - 1 = 5\\\\h = 10\end{array} \right.\\\\ \Rightarrow V = 5 \times 10 = 50\end{array}\)

\(\begin{array}{l}\left\{ \begin{array}{l}S = 0/8 \times 0/8 \times 3/14 = 2/0096\\\\h = 2\end{array} \right.\\\\ \Rightarrow V = 2/0096 \times 2 = 4/0192\end{array}\)

این منبع 4/0192 متر مکعب آب می گیرد.

ابتدا حجم جعبه ی دستمال کاغذی را محاسبه می کنیم:

\(\begin{array}{l}\left\{ \begin{array}{l}S = 12 \times 25 = 300\\\\h = 5\end{array} \right.\\\\ \Rightarrow V = 300 \times 5 = 1500\end{array}\)

این جعبه، 1500 سانتی متر مکعب حجم دارد.

سپس حجم کارتن را محاسبه می کنیم:

\(V = (50 \times 30) \times 24 = 36000\)

حالا حجم کارتن را بر حجم جعبه دستمال کاغذی تقسیم کرده تا مشخص شود که چند تا از این جعبه ها در این کارتن جا می گیرد:

\(\frac{{36000}}{{1500}} = 24\)

در یک کارتن 24 جعبه دستمال کاغذی قرار می گیرد.