Cho hình chóp S.ABCD sao cho hai tam giác ADB và D...

A

- Hướng dẫn giải

\({V_{SABD}} = {V_{SBCD}} = \frac{1}{2}{V_1}\)

\(\frac{{{V_{SMNQ}}}}{{{V_{SABD}}}} = \frac{1}{2}.\frac{1}{3}.\frac{1}{5} = \frac{1}{{30}} \Rightarrow {V_{SMNQ}} = \frac{1}{{30}}.{V_{SABD}} = \frac{1}{{60}}{V_1}\)

\(\frac{{{V_{SNPQ}}}}{{{V_{SBCD}}}} = \frac{1}{3}.\frac{1}{4}.\frac{1}{5} = \frac{1}{{60}} \Rightarrow {V_{SNPQ}} = \frac{1}{{60}}.{V_{SBCD}} = \frac{1}{{120}}{V_1}\)

\({V_{SMNPQ}} = \frac{1}{{60}}{V_1} + \frac{1}{{120}}{V_1} = \frac{1}{{40}}{V_1} \Rightarrow {V_1} = 40{V_{SMNPQ}}\)