Constructions Case Study Based Questions 02 Term II

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.As it turns out, the road the engineer will be building and the road it will connect to both represent characteristics of a circle that have their own name. The road/bridge that already exists is called a secant of the circular lake, and the road the engineer is going to build is called the tangent of the circular 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

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