NCERT Solutions Class 9 Maths Chapter 13 Surface Areas and Volumes | Fuzy Math Academy

Introduction

Hey, let's dive into Class 9 Maths Chapter 13 on Surface Areas and Volumes. This chapter covers 3D shapes like cuboids, cylinders, cones, spheres – think practical stuff like calculating paint for walls or water in tanks. I've got all NCERT exercise solutions here with clear steps so you can follow along easily.

Key Formulas

Cuboid: TSA = 2(lb + bh + hl), Volume = l × b × h.
Cylinder: CSA = 2πrh, TSA = 2πr(r + h), Volume = πr²h.
Cone: CSA = πrl (where l = √(r² + h²)), TSA = πr(l + r), Volume = (1/3)πr²h.
Sphere: SA = 4πr², Volume = (4/3)πr³.
Hemisphere: CSA = 2πr², TSA = 3πr², Volume = (2/3)πr³.

Exercise 13.1 Solutions

Q1: Open plastic box: l=1.5m, b=1.25m, h=0.65m. (i) Sheet area? (ii) Cost Rs20/m².
Area = lb + 2(bh + hl) = 1.5×1.25 + 2(1.25×0.65 + 1.5×0.65) = 1.875 + 1.95 + 1.95 = 5.45 m². Cost = 5.45×20 = Rs 109.

Q2: Room 5×4×3m, whitewash walls+ceiling Rs7.50/m².
Area = 2(5×3 + 4×3) + 5×4 = 74 m². Cost = 74×7.50 = Rs 555.

Q3: Hall perimeter 250m, walls Rs10/m² = Rs15,000. Height?
Area = 250h ×10 = 15,000 → h=6m.

Q4: 9.375m² paint, bricks 22.5×10×7.5cm. Bricks needed?
Brick TSA = 0.09375m². Bricks = 9.375/0.09375 = 100.

Q5: Cube 10cm edge vs cuboid 12.5×10×8cm. Lateral SA & TSA comparison.
Cube lateral=400cm², cuboid=360cm² (cube more). Cube TSA=600cm², cuboid=610cm² (cube less).

Q6: Greenhouse 30×25×25cm glass area & tape for edges.
TSA=4250cm², tape=320cm.

Q7: 250 big boxes 25×20×5cm + 250 small 15×12×5cm, +5% waste, Rs4/1000cm².
Total area after waste=546,000cm². Cost=Rs 2,184.

Q8: Car shelter 4×3m base, 2.5m high tarpaulin.
Area=47m².

Exercise 13.2 Solutions (Cylinders)

Q1: h=14cm, CSA=88cm². Diameter? (π=22/7)
r=1cm, d=2cm.

Q2: Closed tank h=1m, d=140cm. Sheet?
TSA=7.48m².

Q3: Pipe l=77cm, inner d=4cm, outer=4.4cm. CSAs & TSA.
Inner CSA=968cm², outer=1,064.8cm², TSA=2,038.08cm².

Q4: Roller d=84cm, l=120cm, 500 revs. Area?
1,584m².

Q5: Pillar d=50cm, h=3.5m paint CSA Rs12.50/m².
Cost=Rs68.75.

Q6: CSA=4.4m², r=0.7m. h=1m.

Q7: Well d=3.5m, depth=10m plaster Rs40/m².
Cost=Rs4,400.

Q8: Pipe l=28m, d=5cm radiating surface=4.4m².

Q9: Tank d=4.2m, h=4.5m CSA & steel +1/12 waste.
CSA=59.4m², steel=95.04m².

Q10: Lampshade d=20cm, h=30cm +2.5cm margins. Cloth=2,200cm².

Q11: 35 penholders r=3cm, h=10.5cm cardboard=7,920cm².

Exercise 13.3 Solutions (Cones)

Q1: d=10.5cm, l=10cm CSA=165cm².

Q2: l=21m, d=24m TSA=1,244.57m².

Q3: CSA=308cm², l=14cm → r=7cm, TSA=462cm².

Q4: Tent h=10m, r=24m → l=26m, canvas cost Rs1,37,280.

Q5: Tent h=8m, r=6m tarpaulin 3m wide +20cm waste → 63m.

Q6: Tomb l=25m, d=14m whitewash Rs210/100m²=Rs1,155.

Q7: 10 caps r=7cm, h=24cm sheet=5,500cm².

Q8: 50 cones d=40cm, h=1m paint Rs12/m²=Rs384.34.

Exercise 13.4 Solutions (Spheres)

Q1: SA for r=10.5cm=1,386cm²; 5.6cm=394.24cm²; 14cm=2,464cm².

Q2: d=14cm=616cm²; 21cm=1,386cm²; 3.5cm=38.5cm².

Q3: Hemisphere r=10cm TSA=942cm² (π=3.14).

Q4: Balloon r 7→14cm SA ratio 1:4.

Q5: Bowl d=10.5cm tin Rs16/100cm²=Rs27.72.

Q6: SA=154cm² → r=3.5cm.

Q7: Moon d=1/4 earth SA 1:16.

Q8: Bowl inner r=5cm thick 0.25cm outer CSA=173.25cm².

Q9: Cylinder enclosing sphere: SA ratio 1:1.

Exercise 13.5 Solutions (Volumes)

Q1: 12 matchboxes=180cm³.

Q2: Tank 6×5×4.5m=1,35,000L.

Q3: Vessel 10×8m, 380m³ → h=4.75m.

Q4: Pit 8×6×3m dig Rs30/m³=Rs4,320.

Q5: 50,000L tank l=2.5m h=10m → b=2m.

Q6: Village tank 20×15×6m=3 days.

Q7: Godown 40×25×15m crates 1.5×1.25×0.5m=16,000.

Q8: Cube 12cm to 8 equal → side=6cm, SA 4:1.

Q9: River 3×40m 2km/h=4,000m³/min.

Exercise 13.6 Solutions (Combinations)

Q1: Cylinder circ=132cm h=25cm=34.65L.

Q2: Pipe inner/outer d=24/28cm l=35cm mass 0.6g/cm³=3.432kg.

Q3: Tin vs cylinder capacity diff=85cm³.

Q4: CSA=94.2cm² h=5cm → r=3cm V=141.3cm³.

Q5: Paint Rs2,200 Rs20/m² h=10m → r=1.75m capacity=96.25m³.

Q6: Closed cyl h=1m 15.4L sheet=0.4708m².

15 FAQs

1. Cuboid TSA formula? 2(lb + bh + hl).

2. Cylinder volume? πr²h.

3. Cone slant height? √(r² + h²).

4. Sphere SA? 4πr².

5. Ex13.1 Q1 area? 5.45m².

6. Roller area Ex13.2 Q4? 1,584m².

7. Tent l Ex13.3 Q4? 26m.

8. Balloon ratio Ex13.4 Q4? 1:4.

9. Tank litres Ex13.5 Q2? 1,35,000L.

10. Pipe mass Ex13.6 Q2? 3.432kg.

11. Godown crates Ex13.5 Q7? 16,000.

12. Well cost Ex13.2 Q7? Rs4,400.

13. Hemisphere TSA? 3πr².

14. Cube SA ratio Ex13.5 Q8? 4:1.

15. Penholders Ex13.2 Q11? 7,920cm².

Practice these, and you'll nail the chapter. For live doubt clearing, check Fuzy Math Academy classes.