Discussion
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- Question
- A sphere of radius r has the same volume as that of a cone with circular base of radius r. Find the height of the cone.?
Options- A. 2r
- B. r/3
- C. 4r
- D. (2/3)r
- Correct Answer
- 4r
ExplanationGiven that,
Volume of sphere = Volume of cone
? (4/3)?r3 = (1/3)?r2h
? 4r = h - 1. Find the total surface area of a pyramid having a slant height of 8 cm and a base which is a square of side 4 cm (in cm 2)?
Options- A. 80
- B. 64
- C. 72
- D. 84 Discuss
- 2. A hemisphere has 3 cm radius. Calculate its volume.?
Options- A. 4/3 ? cm3
- B. 13 ? cm3
- C. 18? cm3
- D. 19/? cm3 Discuss
- 3. What will be the surface area of the sphere having 4 cm radius?
Options- A. 64? sq cm
- B. 69? sq cm
- C. 32? sq cm
- D. 35? sq cm Discuss
- 4. The side of a cube measures 9 cm. What will be the diagonal of the cube (in cm)?
Options- A. 5?3
- B. 7?3
- C. 9?3
- D. 3?3 Discuss
- 5. A cylinder and a cone have the same height and same radius of the base. The ratio between the volumes of the cylinder and the cone is?
Options- A. 1 : 3
- B. 3 : 1
- C. 1 : 2
- D. 2: 1 Discuss
- 6. A tank 3 m long, 2 m wide and 1.5 m deep is dug in a field 22 m long and 14 m wide. If the earth dug out is evenly spread out over the field, the rose in level of the field will be?
Options- A. 0.299 cm
- B. 0.29 cm
- C. 2.98 cm
- D. 4.15 cm Discuss
- 7. Two cubes have volumes in the ratio 1: 27, The ratio of their surface areas is?
Options- A. 1 : 3
- B. 1 : 8
- C. 1 : 9
- D. 1 : 18 Discuss
- 8. If each edge of a cube is increased in increased by 50%, the percentage increase in surface area is?
Options- A. 50 %
- B. 75 %
- C. 100 %
- D. 125 % Discuss
- 9. The difference in volumes of two cubes is 152 m 3 and the difference in their one face areas is 20 m 2. If the sum of their edge is 10 m, the product of their edge is?
Options- A. 21
- B. 24
- C. 36
- D. 48 Discuss
- 10. The sun of length, breadth and depth of a cuboid is 19 cm and its diagonal is 5 ? 5 cm. Its surface area is?
Options- A. 361 cm2
- B. 125 cm2
- C. 236 cm2
- D. 486 cm2 Discuss
Volume and Surface Area problems
Search Results
Correct Answer: 80
Explanation:
Total surface area of the pyramid
= [1/2(perimeter of the base) (Slant height) ] + Area of the base
= 1/2 (4) (4) (8) + 42 = 80 cm2
Correct Answer: 18? cm3
Explanation:
volume = (2/3)?r3
= (2/3) x ? x 33
= (2/3) x ? x 27
= 18? cm3
Correct Answer: 64? sq cm
Explanation:
Required surface area = 4?r2
= 4 x ? x 42 = 664? sq cm
Correct Answer: 9?3
Explanation:
Given, side of cube, a = 9
? Diagonal of cube = a?3 = 9?3
Correct Answer: 3 : 1
Explanation:
Ratio of their volumes = [?r2h] / [(1/3)?r2h] = 3/1
= 3 : 1
Correct Answer: 2.98 cm
Explanation:
Earth dug out = (3 x 2 x 1.5 ) m3 = 9 m3
Area on which earth has been spread = (22 x 14 - 3 x 2 ) m2 = 302 m2
? Rise in level = Volume/Area = (9/302) m = (9 x 100/302) cm = 2.98 cm
Correct Answer: 1 : 9
Explanation:
Let the volume be x3 and 27x3
? Their edges are x and 3x
Now Ratio of their surface area = 6x2 : 54x2 = 1 : 9
Correct Answer: 125 %
Explanation:
Let original length of cube = L
Then, its surface area = 6L2
New edge = (150 x L)/10 = 3L/2
New surface area = 6 x (3L/2)2 = (6 x 9 x L2)/4 = (27/2) x L2
Increase in surface area = (27/2 - 6) x L2 = 15 x L2/2
? Increase percent = (15 x L2/2 ) / (6L2) x 100 % = 125 %
Correct Answer: 24
Explanation:
Let the edges of the two cubes be x and y metres
Then, x3 - y3 = 152
and x2 - y2 = 20
Also, x + y = 10
So, x - y = (x2 - y2) / (x + y) = 20/10 = 2
Now, (x3 - y3) / (x - y) = 152/2
? x2 + y2 + xy = 76
? (x + y)2 - xy = 76
? xy = (x + y)2 - 76 = (10)2 - 76 = 24
Correct Answer: 236 cm2
Explanation:
? l + b + h = 19
and l2 + b2 + h2 = (5?5)2 = 125
? (l + b + h)2 = (19)2
? (l2 + b2+ h2) + 2(lb + bh + lh) = 361
? 2 (lb + bh + lh) = (361 - 125) = 236
? Surface area = 236 cm2
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