# Mensuration

1. The respective ratio of curved surface area and total surface area of a cylinder is 12 : 19. If the curved surface area of the cylinder is 4752 cm2 , what is its height? (In cm)

A) 24    B) 36    C) 25      D) 26      E) 21

h = 12x

r = 7x

2πrh = 4752

2× 22/7 × 7x  × 12x = 4752

x 2 = 9 ⇒ x = 3

Height = 12x = 12 × 3 = 36

Ans: B

2. The difference between the total cost of fencing, at the rate of Rs.5 per meter, a circular field and a square field is Rs.160. What is the area of the circular field, if the radius of the circular field is equal to the side of the square field? (In meter square)

A) 1386    B) 346.5    C) 616    D) 2464     E) 154

Ans: C

3. The difference between the total surface area of the cylinder to the curved surface area of the cylinder is 1232. The radius of the cylinder is equal to the radius of the cone. The height of the cone is 18, and then finds the volume of the cone.

A) 3656    B) 3696    C) 3756    D) 3773     E) 850

Explanation: 2πr (h + r) − 2πrh =1232

2πr(h + r − h) = 1232

r 2 = 28 × 7

r = 14

Volume of the cone = 1/3 π × r 2 × h

1/3 x 22/7 x 14 x 14 x 18 = 3696

Ans: B

4. Length of the diagonal of one of the sides of cube A is 6√3 cm. If the length of each side of cube B is 33.33% more than that of cube A, what is the sum of the total surface area of cube A and total surface area of cube B? (In cm2 )

A) 600    B) 726    C) 984   D) 1024    E) 864

Side of th ecube (a) = 6

Side of the cube b = 6 x 4/3 = 8

= Total surface area of cube A + total surface area of cube B

= 6 × (6)2 + 6(8)

= 600

Ans: A

5. Two cones have their heights in the ratio 2 : 3 and the radius of their bases in the ratio 3 : 2. Find the ratio of their volumes.

A) 4 : 3     B) 3 : 2     C) 1 : 3     D) 3 : 1     E) 3 : 5

Explanation: 1/3 π × r12 × h : 1/3× π × r2 2 × h

(3)2 × 2 : (2)2 × 3

9 × 2 : 4 × 3 = 3 : 2

Ans: B

6. The sum of the radius and height of a cylinder is 18 m. If the total surface area of the cylinder is 792 m2 , what is the volume of the cylinder? (In m3 )

A) 1848     B) 1716    C) 1448     D) 1694    E) 1724

Explanation: r + h = 18

2πr(h + r) = 792

2 × 22/7 × r(18) = 792

r = 7

h = 11

Volume of cylinder = π × r 2 × h

=  22/7 × 7 × 7 × 11 = 1694

Ans: D

7. There are two rectangles A and B. Length of rectangle B is 20% more than that of rectangle A and the breadth of rectangle B is 25% more than that of rectangle A. If the difference between the areas of both the rectangles is 200m2 , what is the area of rectangle A? (In m2

A) 800      B) 400     C) 650       D) 300    E) 240

Explanation:  A      :     B

Length : 5x          6x

30xy − 20xy = 200

xy = 20 ]

Area of rectangle A = 5x × 4y

= 5 × 4 × 20

= 400

Ans: B

8. The circumference of a circle is 10% more than the perimeter of a square. If the difference between the area of the circle and that of the square is 486 cm2 , how much does the diagonal of the square measure? (In cm)

A) 15√ 2     B) 30      C) 30√2     D) 15     E) 25

154x2 − 100x2 = 486

54x2 = 486

x2 = 9 ⇒ x = 3

a = 10x = 10 × 3 = 30

Diagonal of square = a√ 2 = 30√ 2

Ans: C

9. Three cubes of side ‘a’ melted into cuboid of volume 1536 m3 . If the side of cube is reduced by 2 m, then find the total surface area of cube.

A) 248     B) 144    C) 216    D) 288     E)188

Explanation: 3a3 = 1536

a 3 = 512

a = 8

Side of the cube a = 8 − 2 = 6

Total surface area of the cube = 6a2

= 6 × 36 = 216

Ans: C

10. The respective ratio of curved surface area and total surface area of a cylinder is 9 : 16. If the curved surface area of the cylinder is 1584 cm2 , what is its height? (In cm)

A) 24    B) 18     C) 20     D) 16    E) 21

h = 9x, r = 7x

Curved surface area of cylinder 2πrh = 1584

2 x 22/7 x 7x X 9x = 1584

x 2 = 4 ⇒ x = 2

Height = 9x = 9 × 2 = 18

Ans: B

11. The base of a right prism is an equilateral triangle. If the lateral surface area and volume are 150 cm2 , 50√ 3 cm3 respectively then the side of base of the prism is?

A) 4 cm      B) 8 cm      C) 7 cm     D) 14 cm    E) 16 cm

Explanation: Lateral surface area of prism = primeter of base × height

150 = 3ah

ah = 50

Volume of the prism = area of base × height

Ans: A

12. The respective ratio of numeric values of curved surface area and volume of a right circular cylinder is 1 : 6. If the height of the cylinder is 1.5 times of its radius, what is the total surface area of the cylinder? (In m2 )

1) 360π     2) 660π     3) 720π     4) 960π    5) 900π

Explanation: height and radius of cylinder = 1.5 : 1

= 3 : 2

x = 6

height of cylinder = 3x = 3 × 6 = 18

radius of cylinder = 2x = 2 × 6 =12

total surface area of cylinder = 2πr(h + r)

= 2 × π × 12(12 + 18)

= 720π

Ans: C

13. The circumference of the circle is 440 cm and radius of the circle is 40% more than the length of the rectangle. What is the area of the rectangle if perimeter of the rectangle is 250 cm?

A) 3750     B) 2300     C) 2450   D) 1900     E) 1750

Explanation: 2πr = 440

2 X 22/7 X r = 440

length of rectangle = 70/140 X 100 = 50

2(l + b) = 250

2(50 + b) = 250

b = 75

area of rectangle = 75 × 50 = 3750

Ans: A

14. The volume of sphere is 310464 cm3 and radius of the sphere is 40% more than the radius of cylinder. The ratio of height and radius of the cylinder is 3 : 5, and then what is volume of cylinder?

A) 50914.28     B) 40914.28      C) 30914.28     D) 20914.28     E) 10914.28

Explanation: Volume of the sphere = 4/3 πr 3

= 50914.28

Ans: A

Posted Date : 25-04-2023

గమనిక : ప్రతిభ.ఈనాడు.నెట్‌లో కనిపించే వ్యాపార ప్రకటనలు వివిధ దేశాల్లోని వ్యాపారులు, సంస్థల నుంచి వస్తాయి. మరి కొన్ని ప్రకటనలు పాఠకుల అభిరుచి మేరకు కృత్రిమ మేధస్సు సాంకేతికత సాయంతో ప్రదర్శితమవుతుంటాయి. ఆ ప్రకటనల్లోని ఉత్పత్తులను లేదా సేవలను పాఠకులు స్వయంగా విచారించుకొని, జాగ్రత్తగా పరిశీలించి కొనుక్కోవాలి లేదా వినియోగించుకోవాలి. వాటి నాణ్యత లేదా లోపాలతో ఈనాడు యాజమాన్యానికి ఎలాంటి సంబంధం లేదు. ఈ విషయంలో ఉత్తర ప్రత్యుత్తరాలకు, ఈ-మెయిల్స్ కి, ఇంకా ఇతర రూపాల్లో సమాచార మార్పిడికి తావు లేదు. ఫిర్యాదులు స్వీకరించడం కుదరదు. పాఠకులు గమనించి, సహకరించాలని మనవి.