## Mathematics TERM II

## Constructions

## Class 10 Session 2021-2022

## Case Study Questions 02

The construction of a road is in progress. A road already exists through a forest that goes over a circular lake. The engineer wants to build another road through the forest that connects this road, but does not go through the lake.

1. Refer to the above, if PT = 12 km and PA = 9 km, then the length of existing bridge is

(a) 7 km

(b) 9 km

(c) 12 km

(d) 16 km

(a) 7 km

2. Refer to the above if the length of existing bridge is 5 km and the length of the existing road outside the lake is 4 km,

then the length of the road under construction is

(a) 4 km

(b) 6 km

(c) 10 km

(d) 14 km

(b) 6 km

3. Refer to the question (2) if the road under construction, PT is 6 km and it is inclined at an angle of 30° to the line joining the centre, the radius of the lake is

(a) `3\sqrt{3}` km

(b) `4\sqrt{3}` km

(c) `2\sqrt{3}` km

(d) `5\sqrt{3}` km

(c) `2\sqrt{3}` km

4. Refer to the question (3) above, the circumference of the lake is

(a) `2\sqrt{3}\pi` km

(b) `3\sqrt{3}\pi` km

(c) `4\sqrt{3}\pi` km

(d) `5\sqrt{3}\pi` km

(c) `4\sqrt{3}\pi` km

5. Refer to the question (3) above, the area of the lake is

(a) `12\pi` sq. km

(b) `16\pi` sq. km

(c) `18\pi` sq. km

(d) `9\pi` sq. km

(a) `12\pi` sq. km