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正方体ABCD-A1B1C1D1中,O是上底面ABCD中心,若棱长为a,则三棱锥O-AB1D1的体积为.
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答案和解析
如图,在正方体ABCD-A11B11C11D11中,
O是上底面ABCD的中心,棱长为a,
∴对角线AC⊥平面BDD11B11,
∴三棱锥O-AB11D11的体积为
V三棱锥O-AB1D1=
•S△OB1D1•AO
=
•
B1D1•OO1•AO
=
•
•
a•a•
a
=
a3.
故答案为:
a3. V三棱锥O-AB1D1=
•S△OB1D1•AO
=
•
B1D1•OO1•AO
=
•
•
a•a•
a
=
a3.
故答案为:
a3. 三棱锥O-AB1D1=
•S△OB1D1•AO
=
•
B1D1•OO1•AO
=
•
•
a•a•
a
=
a3.
故答案为:
a3. 1D1=
•S△OB1D1•AO
=
•
B1D1•OO1•AO
=
•
•
a•a•
a
=
a3.
故答案为:
a3. 1=
•S△OB1D1•AO
=
•
B1D1•OO1•AO
=
•
•
a•a•
a
=
a3.
故答案为:
a3.
1 1 13 3 3•S△OB1D1•AO
=
•
B1D1•OO1•AO
=
•
•
a•a•
a
=
a3.
故答案为:
a3. S△OB1D1•AO
=
•
B1D1•OO1•AO
=
•
•
a•a•
a
=
a3.
故答案为:
a3. △OB1D1•AO
=
•
B1D1•OO1•AO
=
•
•
a•a•
a
=
a3.
故答案为:
a3. 1D1•AO
=
•
B1D1•OO1•AO
=
•
•
a•a•
a
=
a3.
故答案为:
a3. 1•AO
=
•
B1D1•OO1•AO
=
•
•
a•a•
a
=
a3.
故答案为:
a3.
1 1 13 3 3•
B1D1•OO1•AO
=
•
•
a•a•
a
=
a3.
故答案为:
a3.
1 1 12 2 2B11D11•OO11•AO
=
•
•
a•a•
a
=
a3.
故答案为:
a3.
1 1 13 3 3•
•
a•a•
a
=
a3.
故答案为:
a3.
1 1 12 2 2•
a•a•
a
=
a3.
故答案为:
a3.
2 2 2a•a•
a
=
a3.
故答案为:
a3.
2 2 22 2 2a
=
a3.
故答案为:
a3.
1 1 16 6 6a3.
故答案为:
a3. 3.
故答案为:
a3.
1 1 16 6 6a3. 3.

O是上底面ABCD的中心,棱长为a,
∴对角线AC⊥平面BDD11B11,
∴三棱锥O-AB11D11的体积为
V三棱锥O-AB1D1=
1 |
3 |
=
1 |
3 |
1 |
2 |
=
1 |
3 |
1 |
2 |
2 |
| ||
2 |
=
1 |
6 |
故答案为:
1 |
6 |
1 |
3 |
=
1 |
3 |
1 |
2 |
=
1 |
3 |
1 |
2 |
2 |
| ||
2 |
=
1 |
6 |
故答案为:
1 |
6 |
1 |
3 |
=
1 |
3 |
1 |
2 |
=
1 |
3 |
1 |
2 |
2 |
| ||
2 |
=
1 |
6 |
故答案为:
1 |
6 |
1 |
3 |
=
1 |
3 |
1 |
2 |
=
1 |
3 |
1 |
2 |
2 |
| ||
2 |
=
1 |
6 |
故答案为:
1 |
6 |
1 |
3 |
=
1 |
3 |
1 |
2 |
=
1 |
3 |
1 |
2 |
2 |
| ||
2 |
=
1 |
6 |
故答案为:
1 |
6 |
1 |
3 |
=
1 |
3 |
1 |
2 |
=
1 |
3 |
1 |
2 |
2 |
| ||
2 |
=
1 |
6 |
故答案为:
1 |
6 |
=
1 |
3 |
1 |
2 |
=
1 |
3 |
1 |
2 |
2 |
| ||
2 |
=
1 |
6 |
故答案为:
1 |
6 |
=
1 |
3 |
1 |
2 |
=
1 |
3 |
1 |
2 |
2 |
| ||
2 |
=
1 |
6 |
故答案为:
1 |
6 |
=
1 |
3 |
1 |
2 |
=
1 |
3 |
1 |
2 |
2 |
| ||
2 |
=
1 |
6 |
故答案为:
1 |
6 |
=
1 |
3 |
1 |
2 |
=
1 |
3 |
1 |
2 |
2 |
| ||
2 |
=
1 |
6 |
故答案为:
1 |
6 |
1 |
3 |
1 |
2 |
=
1 |
3 |
1 |
2 |
2 |
| ||
2 |
=
1 |
6 |
故答案为:
1 |
6 |
1 |
2 |
=
1 |
3 |
1 |
2 |
2 |
| ||
2 |
=
1 |
6 |
故答案为:
1 |
6 |
1 |
3 |
1 |
2 |
2 |
| ||
2 |
=
1 |
6 |
故答案为:
1 |
6 |
1 |
2 |
2 |
| ||
2 |
=
1 |
6 |
故答案为:
1 |
6 |
2 |
| ||
2 |
=
1 |
6 |
故答案为:
1 |
6 |
| ||
2 |
2 |
2 |
2 |
=
1 |
6 |
故答案为:
1 |
6 |
1 |
6 |
故答案为:
1 |
6 |
故答案为:
1 |
6 |
1 |
6 |
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