Surface Areas and Volumes — Andhra Pradesh (SSC) Class 9 Mathematics Solutions (Free)
Free step-by-step Andhra Pradesh (SSC) Class 9 Mathematics solutions for "Surface Areas and Volumes" — important questions with detailed answers, download PDF for board exam preparation.
TL;DR: Free step-by-step Andhra Pradesh (SSC) Class 9 Mathematics solutions for "Surface Areas and Volumes" — important questions with detailed answers, down…
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Q1: Find the total surface area and volume of a cuboid (rectangular prism) with length 12 cm, breadth 8 cm, and height 6 cm.
Step 1: Cuboid dimensions:
Length (l) = 12 cm
Breadth (b) = 8 cm
Height (h) = 6 cm
Step 2: Total Surface Area of Cuboid:
Formula: Total Surface Area = 2(lb + bh + hl)
Step 3: Calculate each product:
lb = 12 × 8 = 96 cm²
bh = 8 × 6 = 48 cm²
hl = 6 × 12 = 72 cm²
Step 4: Sum of products:
lb + bh + hl = 96 + 48 + 72 = 216 cm²
Step 5: Calculate surface area:
Total Surface Area = 2 × 216 = 432 cm²
Step 6: Volume of Cuboid:
Formula: Volume = l × b × h
Volume = 12 × 8 × 6
Volume = 96 × 6
Volume = 5…
Q2: A cylinder has radius 7 cm and height 10 cm. Find its curved surface area, total surface area, and volume.
Step 1: Cylinder dimensions:
Radius (r) = 7 cm
Height (h) = 10 cm
Step 2: Curved Surface Area (Lateral Surface Area):
Formula: Curved Surface Area = 2πrh
Curved Surface Area = 2 × π × 7 × 10
Curved Surface Area = 140π cm²
Curved Surface Area ≈ 140 × 3.14159 ≈ 439.82 cm²
Step 3: Area of Two Circular Bases:
Area of one circle = πr²
Area of one circle = π × 7²
Area of one circle = 49π cm²
Area of two circles = 2 × 49π = 98π cm²
Area of two circles ≈ 98 × 3.14159 ≈ 307.88 cm²
Step 4: Total Surfac…
Q3: A cone has base radius 5 cm, height 12 cm. Find the slant height, curved surface area, total surface area, and volume.
Step 1: Cone dimensions:
Base radius (r) = 5 cm
Height (h) = 12 cm
Slant height (l) = ?
Step 2: Find slant height using Pythagoras theorem:
The slant height, radius, and height form a right triangle.
l² = r² + h²
l² = 5² + 12²
l² = 25 + 144
l² = 169
l = 13 cm
Step 3: Curved Surface Area (Lateral Surface Area):
Formula: Curved Surface Area = πrl
Curved Surface Area = π × 5 × 13
Curved Surface Area = 65π cm²
Curved Surface Area ≈ 65 × 3.14159 ≈ 204.20 cm²
Step 4: Area of Circular Base:
Area of …
Q4: A sphere has radius 6 cm. Find its surface area and volume.
Step 1: Sphere radius:
r = 6 cm
Step 2: Surface Area of Sphere:
Formula: Surface Area = 4πr²
Surface Area = 4 × π × 6²
Surface Area = 4 × π × 36
Surface Area = 144π cm²
Surface Area ≈ 144 × 3.14159 ≈ 452.39 cm²
Step 3: Volume of Sphere:
Formula: Volume = (4/3)πr³
Volume = (4/3) × π × 6³
Volume = (4/3) × π × 216
Volume = (4/3 × 216) × π
Volume = (864/3) × π
Volume = 288π cm³
Volume ≈ 288 × 3.14159 ≈ 904.78 cm³
Step 4: Verification:
For r = 6:
4πr² = 4π(6)² = 144π ✓
(4/3)πr³ = (4/3)π(6)³ = (4/3…
Q5: A hemisphere has radius 8 cm. Find its curved surface area, total surface area (curved + base), and volume.
Step 1: Hemisphere radius:
r = 8 cm
Step 2: Curved Surface Area (curved part only):
Formula: Curved Surface Area = 2πr²
Curved Surface Area = 2 × π × 8²
Curved Surface Area = 2 × π × 64
Curved Surface Area = 128π cm²
Curved Surface Area ≈ 128 × 3.14159 ≈ 402.12 cm²
Step 3: Area of Circular Base:
Area of base = πr²
Area of base = π × 8²
Area of base = 64π cm²
Area of base ≈ 64 × 3.14159 ≈ 201.06 cm²
Step 4: Total Surface Area:
Total Surface Area = Curved Surface Area + Base Area
Total Surface …
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