Answer:
1. Answer: (c) same
2. Answer: (C) remain unaltered
Explanation: During conversion of one solid shape to another, the volume of the new shape will remain unaltered.
3. Answer: (b) 20: 27
Explanation: Given that, the radii of two cylinders are in the ratio of 2:3
Hence, r1= 2r, r2 = 3r
Also, given that, the height of two cylinders are in the ratio 5:3.
Hence, h1 = 5h, h2 = 3h
The ratio of the volume of two cylinders = V1/V2
= πr12h1/πr22h2
= [(2r)2(5h)]/[(3r)2(3h)]
Ratio of their volumes =(20r2h)/(27r2h) = 20/27 = 20: 27.
4. Answer: (b) πr(l+(r/4))
Explanation: The total surface area of cone = πr(l+r) square units.
If r = r/2 and l= 2l, then the TSA of cone becomes,
TSA of cone = π(r/2)[(2l+(2/r)]
=π[(rl)+(r2/4)]
TSA of new cone =πr[l+(r/4)]
5. Answer: (a) 512 m3
Explanation: The lateral surface area of cube = 4a2
4a2= 256
a2 = 256/4 =64
a = 8 m
Hence, the volume of cube = a3 cube units
V = 83 = 512 m3.
6. Answer: (b) \(\sqrt{abc}\)
7. Answer: (b) 1920
Explanation: Volume of Plank = 400 cm×50cm×20cm=400000cm3
Volume of pits = 1600cm×1200cm×400cm = 768000000cm3
Number of planks = Volume of planks/Volume of pits
= 768000000/400000
Hence, the number of pits = 1920
8. Answer: (b) 2.1 cm
Explanation: Given that the height of cone = 8.4 cm
Radius of cone = 2.1 cm
Also, given that the volume of cone = volume of a sphere
(1/3)πr2h = (4/3)πr3
(1/3)π(2.1)2(8.4) = (4/3)πr3
37.044= 4r3
r3= 37.044/4
r3= 9.261
r = 2.1
Therefore, the radius of the sphere is 2.1 cm.
9. Answer: (a) 15m
Explanation: Given: l=10m, b= 10m, h= 5m
The length of the longest pole = √[102+102+52]
= √(100+100+25) = √225 = 15 m.
10. Answer: (c) 64 cm3
Explanation: We know that the TSA of the cone = 6a2.
6a2 = 96 cm2
a2 = 96/6 = 16
a =4 cm
The volume of cone = a3 cubic units
V = 43 = 64cm3.
11. Answer: (c) 4/3 π(R3 – r3)
12. Answer: (a) π(R2 – r2)h
13. Answer: (d) 32/3 πr3
14. Answer: (a) 1:4
Explanation: We know that the total surface area of the hemisphere = 3πr2 square units.
If r= 6cm, then TSA = 3π(6)2 = 108π
If r = 12 cm, then TSA = 3π(12)2= 432π
Then the ratio = (108π)/(432π)
Ratio = 1/4, which is equal to 1:4.
15. Answer: (c) 2464 sq.cm
Explanation: Radius of sphere, r = 14 cm
Surface area = 4πr2
= 4 x 22/7 x (14)2 = 2464 sq.cm.
16. Answer: (d) 1244.57 sq.cm
Explanation: Total surface area = πr(l + r)
r = 24/2 = 12 cm
l = 21 cm
TSA = π(12)(21 + 12) = 1244.57 sq.cm
17. Answer: (b) 165 sq.cm
Explanation: Diameter = 10.5, Radius = 10.5/2
Slant height, l = 10cm
Curved surface area of cone = πrl = π(5.25)(10)
CSA = 165 sq.cm
18. Answer: (c) 1 cm
Explanation: Curved surface area of cylinder = 2πrh
2πrh = 4.4
h = 4.4/(2π x 0.7)
h = 1 cm
19. Answer: (a) 2 cm
Explanation: Curved surface area of cylinder = 88 sq.cm
Height = 14 cm
2πrh = 88
r = 88/2πh
r=1 cm
Diameter = 2r = 2cm
20. Answer: (a) 1 : 4
Click here to practice: – Surface Areas and Volumes MCQ Question for Class 9 Maths