Topics

If \( \Large \triangle ABC \) is an equilateral triangle of area \( \Large 36\sqrt{3} cm^{2} \), then area of the inscribed circle is


A) \( \Large 48 \pi cm^{2} \)

B) \( \Large 36 \pi cm^{2} \)

C) \( \Large 24 \pi cm^{2} \)

D) \( \Large 12 \pi cm^{2} \)

Correct Answer:
D) \( \Large 12 \pi cm^{2} \)

Description for Correct answer:

Let a be the side of the equilateral triangle.

Therefore, Its area = \( \Large \frac{a^{2}\sqrt{3}}{4} \)

\( \Large \therefore \frac{a^{2}\sqrt{3}}{4} = 36\sqrt{3} \)

=> \( \Large a^{2} = 36 \times 4 \)

=> \( \Large a = 6 \times 2 = 12 cm\)

Let r be the radius of the inscribed circle.

Therefore, \( \Large r = \frac{\triangle}{s}=\frac{36\sqrt{3}}{\frac{1}{2} \left(12+12+12\right) } = 2\sqrt{3} cm \)

Area of inscribed circle = \( \Large \pi r^{2}= \pi \times \left(2\sqrt{3}\right)^{2}=12 \pi cm^{2} \)


Part of solved Mensuration questions and answers : >> Aptitude >> Mensuration




Comments
No comments available




Similar Questions
1). A ladder 2.0m long is placed in a street so as to reach a window 1.6 m high and on turning the ladder to the other side of a street, it reaches a point 1.2 m high. The width of the street is
A). 2.8 m
B). 2.4 m
C). 2.0 m
D). 1.6 m
-- View Answer
2). Area of the parallelogram given below is
A). 40 sq. cm
B). 20 sq. cm
C). 32 sq. cm
D). 64 sq. cm
-- View Answer
3). If three solid bodies; a sphere, right circular cylinder and a right circular cone are of equal radius and equal surface area, then their heights are in the ratio
A). \( \Large 2 : 1 : 2\sqrt{2} \)
B). \( \Large \sqrt{2} : 1 : 2 \)
C). \( \Large 2 : 1 : 3\sqrt{2} \)
D). \( \Large 6\sqrt{2} : 3\sqrt{3} : 4 \)
-- View Answer
4). A square and an equilateral triangle are inscribed in a circle. If a and b denote lengths of their sides, then
A). \( \Large a^{2}=\frac{b^{2}}{2} \)
B). \( \Large \frac{a^{2}}{2}=b^{2} \)
C). \( \Large 3b^{2}=2a^{2} \)
D). \( \Large 3a^{2}=2b^{2} \)
-- View Answer
5). The slant height of a right circular cone is 10 cm and its height is 8 cm. It is cut by a plane parallel to its base passing through the midpoint of the height. Ratio of the volume of the cone to that of the frustum of the cone cut is
A). 2 : 1
B). 8 : 7
C). 4 : 3
D). 3 : 2
-- View Answer


6). A solid sphere of radius r is sliced by the planes passing through its centre and perpendicular to each other. The total surface area of each of the pieces so formed is
A). \( \Large \frac{2}{3} \pi r^{2} \)
B). \( \Large 2 \pi r^{2} \)
C). \( \Large \frac{4}{3} \pi r^{2} \)
D). \( \Large \pi r^{2} \)
-- View Answer
7). The lateral surface of a cylinder is developed in a square whose diagonal is \( \Large \sqrt{2} \) cm long. Find the volume of the cylinder in cubic centimeters is, if height is 1 cm.
A). \( \Large \frac{1}{4 \pi } \)
B). \( \Large \frac{2}{ \pi } \)
C). \( \Large 3\frac{ \pi }{4} \)
D). \( \Large 2 \pi \)
-- View Answer
8). A plane is drawn parallel to the base of a right circular cone dividing altitude in the ratio of 2 : 1 to chop off the conical part. The chopped off conical part is taller than the remaining portion. The ratio of the volumes of the chopped off part and the remaining part is
A). 1 : 26
B). 2 : 25
C). 4 : 23
D). 8 : 19
-- View Answer
9). Three cubes of metal whose edges are 3cm, 4cm, 5cm, respectively are melted and a new cube is formed. The diagonal of the new cube is
A). \( \Large 4\sqrt{3} cm \)
B). 6 cm
C). \( \Large 6\sqrt{3} cm \)
D). 8 cm
-- View Answer
10). The length, breadth and height of a rectangular solid are 10 cm, 5 cm and 2 cm respectively. Its whole surface area in sq. cms is
A). 7
B). 70
C). 160
D). 280
-- View Answer
Home About Us Terms and Conditions Privacy Policy Contact us