Surface Area and Volume (Copy)
1.
A cuboid measures 12 cm × 8 cm × 5 cm.
Find its volume.
2.
Find the surface area of the cuboid in Q1.
3.
A cube has side length 9 cm.
Find its volume and surface area.
4.
A cuboid has volume 240 cm³. Its base is 12 cm × 5 cm.
Find its height.
5.
A triangular prism has cross-sectional area 30 cm² and length 10 cm.
Find its volume.
6.
A prism has volume 540 cm³ and cross-sectional area 90 cm².
Find its length.
7.
A cylinder has radius 7 cm and height 15 cm.
Find its volume in terms of π.
8.
Find the curved surface area of the cylinder in Q7, in terms of π.
9.
A cylinder has diameter 14 cm and height 20 cm.
Find its total surface area in terms of π.
10.
A metal pipe is hollow, with outer radius 10 cm, inner radius 8 cm, height 12 cm.
Find its volume in terms of π.
11.
A cone has radius 6 cm and slant height 10 cm.
Find its curved surface area in terms of π.
12.
A cone has radius 7 cm and height 24 cm.
Find its volume in terms of π.
13.
A cone has base radius 9 cm and height 12 cm.
Find its slant height.
14.
A cone has base radius 5 cm and slant height 13 cm.
Find its curved surface area.
15.
A sphere has radius 14 cm.
Find its surface area in terms of π.
16.
Find the volume of the sphere in Q15, in terms of π.
17.
A sphere has volume 288π cm³.
Find its radius.
18.
A sphere has surface area 324π cm².
Find its radius.
19.
A pyramid has base area 64 cm² and height 9 cm.
Find its volume.
20.
A square pyramid has base side 12 cm and perpendicular height 10 cm.
Find its volume.
21.
A square pyramid has base side 8 cm and slant height 15 cm.
Find its total surface area.
22.
A cuboid measures 20 cm × 15 cm × 10 cm.
Find its space diagonal.
23.
A triangular prism has equilateral triangular cross-section with side 10 cm and length 15 cm.
Find its volume.
24.
A cone has height 24 cm and slant height 25 cm.
Find its curved surface area.
25.
A hemisphere has radius 7 cm.
Find its curved surface area in terms of π.
26.
A hemisphere has radius 10 cm.
Find its volume in terms of π.
27.
A solid cone has height 36 cm and base radius 15 cm.
Find its volume.
28.
A solid sphere of radius 6 cm is melted down and recast into small spheres of radius 2 cm.
How many small spheres are formed?
29.
A cylindrical tank has diameter 3 m and height 4 m.
Find its volume in cubic metres.
30.
A square-based pyramid has base side 20 m and height 15 m.
Find its volume.
1.
Volume = l × w × h = 12 × 8 × 5 = 480 cm³.
2.
Surface area = 2(lw + lh + wh) = 2(12×8 + 12×5 + 8×5)
= 2(96 + 60 + 40) = 2×196 = 392 cm².
3.
Volume = 9³ = 729 cm³.
Surface area = 6×9² = 6×81 = 486 cm².
4.
Volume = base × height = 12×5×h = 60h.
60h = 240 → h = 4 cm.
5.
Volume = cross-sectional area × length = 30×10 = 300 cm³.
6.
Volume = area × length → 540 = 90×L.
L = 6 cm.
7.
V = πr²h = π×7²×15 = π×49×15 = 735π cm³.
8.
CSA = 2πrh = 2π×7×15 = 210π cm².
9.
TSA = 2πrh + 2πr² = 2π×7×20 + 2π×7² = 280π + 98π = 378π cm².
10.
V = πh(R² − r²) = π×12(10²−8²) = π×12(100−64) = π×12×36 = 432π cm³.
11.
CSA = πrl = π×6×10 = 60π cm².
12.
V = ⅓πr²h = ⅓π×7²×24 = ⅓π×49×24 = 392π cm³.
So 392π cm³.
13.
l = √(r²+h²) = √(9²+12²) = √(81+144) = √225 = 15 cm.
14.
CSA = πrl = π×5×13 = 65π cm².
15.
SA = 4πr² = 4π×14² = 4π×196 = 784π cm².
16.
V = ⁴/₃πr³ = ⁴/₃π×14³ = ⁴/₃π×2744 = 3658.7π cm³.
17.
V = 288π = ⁴/₃πr³.
288 = ⁴/₃r³ → r³ = 288×3/4 = 216 → r = 6 cm.
18.
SA = 324π = 4πr².
r² = 324/4 = 81 → r = 9 cm.
19.
V = ⅓×base×height = ⅓×64×9 = 192 cm³.
20.
Base area = 12² = 144.
V = ⅓×144×10 = 480 cm³.
21.
Base area = 8² = 64.
Slant height = 15.
Each triangular face area = ½×8×15 = 60.
Total 4 triangles = 240.
TSA = 64 + 240 = 304 cm².
22.
Space diagonal = √(l²+w²+h²) = √(20²+15²+10²) = √(400+225+100) = √725 ≈ 26.9 cm.
23.
Equilateral triangle area = (√3/4)×10² = 25√3.
Volume = base area×length = 25√3×15 = 375√3 cm³.
24.
CSA = πrl.
r=15, l=25.
CSA=π×15×25 = 375π cm².
25.
CSA hemisphere = 2πr² = 2π×7² = 98π cm².
So 98π cm².
26.
Volume hemisphere = 2/3πr³ = 2/3π×10³ = 2000/3 π cm³ ≈ 666.7π cm³.
27.
V = ⅓πr²h = ⅓π×15²×36 = ⅓π×225×36 = 2700π cm³.
So 2700π cm³.
28.
V big sphere = ⁴/₃π6³ = ⁴/₃π×216 = 288π.
V small sphere = ⁴/₃π2³ = ⁴/₃π×8 = 32/3π.
No. of spheres = 288π ÷ (32/3π) = 288×3/32 = 27.
So 27 spheres.
29.
Radius = 1.5.
V = πr²h = π×1.5²×4 = π×2.25×4 = 9π ≈ 28.3 m³.
30.
Base = 20² = 400.
V = ⅓×400×15 = 2000 m³.