Mensuration & Geometry - II : Mensuration & Geometry - II
Q.1 : P & Q are points on the circumference of the circle with centre O and radius 14 cm, such that OP = PQ. What is the perimeter of the minor segment bound by the chord PQ? : Q.1 : P & Q are points on the circumference of the circle with centre O and radius 14 cm, such that OP = PQ. What is the perimeter of the minor segment bound by the chord PQ?
Slide 3 : Answer
is 28.66 cms.
Q.2: What is the maximum distance between two parallel chords of length 6 and 8 cm respectively in a circle of diameter 10 cms? : Q.2: What is the maximum distance between two parallel chords of length 6 and 8 cm respectively in a circle of diameter 10 cms?
Slide 5 : Answer
is 7 cm.
Q.3 : Three dimensions of a triangle are integral cm long, with two sides being 17 cm & 7 cm long. How many different such triangles are possible? : Q.3 : Three dimensions of a triangle are integral cm long, with two sides being 17 cm & 7 cm long. How many different such triangles are possible?
Slide 7 : Answer is 13.
Q.4: In triangle PQR, PQ = 10 cm, QR = 8 cm & PR = 6 cm. S is a point on QR such that PS is the angle bisector of RPQ. The angle bisector of PQR intersects PS at W. What is the ratio of lengths of SW to WP? (CAT 1988) : Q.4: In triangle PQR, PQ = 10 cm, QR = 8 cm & PR = 6 cm. S is a point on QR such that PS is the angle bisector of RPQ. The angle bisector of PQR intersects PS at W. What is the ratio of lengths of SW to WP? (CAT 1988)
Slide 9 : Answer
is 1 : 2
Q.5: The ratio of areas of the circumcircle and the incircle of a triangle of dimensions 6 cm, 8 cm and 10 cm is : Q.5: The ratio of areas of the circumcircle and the incircle of a triangle of dimensions 6 cm, 8 cm and 10 cm is
Slide 11 : Answer
is 25 : 4
Q.6 : The length & breadth of a rectangle are 40 mts & 20 mts respectively. A 2 mts wide path is made all around it on the outside. Find the area of the path in sq. metres. : Q.6 : The length & breadth of a rectangle are 40 mts & 20 mts respectively. A 2 mts wide path is made all around it on the outside. Find the area of the path in sq. metres.
Path Original Rectangle : Path Original Rectangle
Answer is 256 sq. metres. : Answer is 256 sq. metres.
Q.7 : The length of a rectangle is 50 metres & its breadth is 40 metres. A 3 metres wide path is made, inside it, in the middle crossing each other. Find the area of path. : Q.7 : The length of a rectangle is 50 metres & its breadth is 40 metres. A 3 metres wide path is made, inside it, in the middle crossing each other. Find the area of path.
Original Rectangle Path : Original Rectangle Path
Answer is 261 sq. mts. : Answer is 261 sq. mts.
Q.8:A square paper is having, an area of 484 sq. cm. The largest possible circle is cut from this paper, what % area of the paper is wasted? (Actual CAT question) : Q.8:A square paper is having, an area of 484 sq. cm. The largest possible circle is cut from this paper, what % area of the paper is wasted? (Actual CAT question)
Slide 19 : Answer is 21.5%
Learn it by heart, it will always be true, that whenever the greatest circle is cut or drawn inside the square, the remaining area will be 21.5% and the area used/inside the circle will be 78.5%. : Learn it by heart, it will always be true, that whenever the greatest circle is cut or drawn inside the square, the remaining area will be 21.5% and the area used/inside the circle will be 78.5%.
Similarly, if the largest possible square is cut/drawn inside the circle, then the % area wasted will be equal to 36.3%. On the same lines, if the largest possible cube is cut from a sphere, then the percentage volume wasted is 63% or the volume of cube is 37% of the volume of the sphere. : Similarly, if the largest possible square is cut/drawn inside the circle, then the % area wasted will be equal to 36.3%. On the same lines, if the largest possible cube is cut from a sphere, then the percentage volume wasted is 63% or the volume of cube is 37% of the volume of the sphere.
Q.9 : Line AB is 6 mts in length & is tangent to the inner one of the 2 concentric circles at point C. It is known that the radii of the two circles are integers. The radius of the outer circle is (in mts) (CAT1993)1. 5 2. 4 3. 6 4. 3 : Q.9 : Line AB is 6 mts in length & is tangent to the inner one of the 2 concentric circles at point C. It is known that the radii of the two circles are integers. The radius of the outer circle is (in mts) (CAT1993)1. 5 2. 4 3. 6 4. 3
Slide 23 : Answer
is 1st option.
Q.10 : 4 horses are tied at the corners of a square of side 14m. The adjacent horses just reach each other. In the central area there is a circular pond having area 20 m2. What is the area (sq m) left ungrazed in the field? (CAT2002) 1. 22 2.42 3.84 4.168 : Q.10 : 4 horses are tied at the corners of a square of side 14m. The adjacent horses just reach each other. In the central area there is a circular pond having area 20 m2. What is the area (sq m) left ungrazed in the field? (CAT2002) 1. 22 2.42 3.84 4.168
Slide 25 : Answer
is 1st option.
Q.11 : 3 identical cones with base radius r are placed on their bases so that each is touching the other two. The radius of the circle drawn through their vertices is (CAT1993)1. < r 2. = r 3. > r 4. Depends on the ht. of the cones. : Q.11 : 3 identical cones with base radius r are placed on their bases so that each is touching the other two. The radius of the circle drawn through their vertices is (CAT1993)1. < r 2. = r 3. > r 4. Depends on the ht. of the cones.
Slide 27 : Answer
is 3rd option.
Q.12: The figure given shows 2 concentric circles with centre O. PQRS is a square inscribed in the outer circle. It also circumscribes the inner circle touching it at points B, C, D and A. What is ratio of the circumference of outer circle to that of polygon ABCD?(CAT 1999) 1. /4 2. 3/2 3. /2 4. : Q.12: The figure given shows 2 concentric circles with centre O. PQRS is a square inscribed in the outer circle. It also circumscribes the inner circle touching it at points B, C, D and A. What is ratio of the circumference of outer circle to that of polygon ABCD?(CAT 1999) 1. /4 2. 3/2 3. /2 4.
Slide 29 : Answer
is 3rd option.
Q.13 : Two circles of radii 15 & 20 cm have their centres 25 cm apart. What is the length of their common chord? (CAT 2002)1.24 cm 2.25cm 3.15 cm 4.20 cm : Q.13 : Two circles of radii 15 & 20 cm have their centres 25 cm apart. What is the length of their common chord? (CAT 2002)1.24 cm 2.25cm 3.15 cm 4.20 cm
Slide 31 : Answer
is 1st option.
Q.14 : A square is drawn by joining the midpoints of the sides of a given square. A 3rd square is drawn inside the 2nd square in the same way & so on indefinitely. If a side of the 1st square is 8 cms., the sum of the areas of all the squares (in cm2) is (CAT 1990)1. 128 2. 120 3. 96 4. None of these : Q.14 : A square is drawn by joining the midpoints of the sides of a given square. A 3rd square is drawn inside the 2nd square in the same way & so on indefinitely. If a side of the 1st square is 8 cms., the sum of the areas of all the squares (in cm2) is (CAT 1990)1. 128 2. 120 3. 96 4. None of these
Slide 33 : Answer
is 1st option.
Q.15 : In a triangle ABC, AB = 6, BC = 8 and AC = 10. A perpendicular dropped from B, meets the side AC at D. A circle of radius BD (with centre B) is drawn. If the circle cuts AB & BC at P and Q respectively, then AP:QC is equal to (CAT Nov 2003). 1. 1:1 2.3:2 3. 4:1 4. 3:8 : Q.15 : In a triangle ABC, AB = 6, BC = 8 and AC = 10. A perpendicular dropped from B, meets the side AC at D. A circle of radius BD (with centre B) is drawn. If the circle cuts AB & BC at P and Q respectively, then AP:QC is equal to (CAT Nov 2003). 1. 1:1 2.3:2 3. 4:1 4. 3:8
Slide 35 : Answer
is 4th option
THANK YOU : THANK YOU