# IMO Level 1- Mathematics Olympiad (SOF) Class 10: Questions 806 - 810 of 968

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## Question 806

### Question

MCQ▾If the radii of the circular ends of a conical bucket are and and the height is The capacity of the bucket is________.

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## Question 807

### Question

MCQ▾The sides MN and MO of a triangle MNO meet the semicircle in P and Q respectively. NO is the diameter of a semicircle. PQ subtends at the center of the semi-circle. The is ________.

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## Question 808

### Question

MCQ▾A sphere is placed in a cone of height 9 cm as shown in figure. The volume of sphere if it touches lateral surface and base of cone is________.

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## Question 809

### Question

MCQ▾In the given figure, FEBD is cyclic quadrilateral and AC is tangent to the circle with center ‘O’ . ED is diameter, the ________.

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## Question 810

### Question

MCQ▾Let PQR be a right triangle in which . QS is the perpendicular from Q on PR. The circle through Q, R, and S is drawn from P to this circle. Given below are the steps of constructions of a pair of tangents. Find out the wrong step.

- Step I: Draw and perpendicular QS from Q on PR.
- Step II: Draw a circle with QR as a diameter. This circle will pass through S.
- Step III: Let O be the mid-point of QR. Join PO.
- Step IV: Draw a circle with PO as diameter. This circle cuts the circle drawn in step II Q at T. join PO, PT and PQ are desired tangents drawn from P to the circle passing through Q, R and S.

### Choices

Choice (4) | Response | |
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a. | Only 1 | |

b. | Only 2 | |

c. | Only 3 | |

d. | Only 4 |