Surface Areas and Volumes — Class 10 Mathematics NCERT Solutions (Free)

Free step-by-step NCERT solutions for Class 10 Mathematics chapter "Surface Areas and Volumes" — 9 important questions with detailed answers for CBSE board exam preparation.

TL;DR: Free step-by-step NCERT solutions for Class 10 Mathematics chapter "Surface Areas and Volumes" — 9 important questions with detailed answers for CBSE…

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Key Questions Covered:

  1. A solid is formed by combining a cylinder and a hemisphere at one end. The cy…
  2. A cone is placed on top of a cylinder. The cylinder has radius 5 cm and heigh…
  3. Find the volume of a frustum of a cone if the radii of the two circular ends …
  4. + 6 more questions in the full chapter

Solutions Summary:

Question Status
A solid is formed by combining a cylinder and a hemispher… ✓ Solved
A cone is placed on top of a cylinder. The cylinder has r… ✓ Solved
Find the volume of a frustum of a cone if the radii of th… ✓ Solved

Showing 3 of 9 questions

Q1: A solid is formed by combining a cylinder and a hemisphere at one end. The cylinder has radius 3.5 cm and height 10 cm. The hemisphere has the same radius. Find the total surface area. (Use π = 22/7)

Step 1: Total surface area = Curved surface area of cylinder + Base area of cylinder + Curved surface area of hemisphere Step 2: Curved surface area of cylinder = 2πrh = 2 × (22/7) × 3.5 × 10 Step 3: = 2 × (22/7) × 35 = 2 × 22 × 5 = 220 cm² Step 4: Base area of cylinder = πr² = (22/7) × (3.5)² Step ...

Q2: A cone is placed on top of a cylinder. The cylinder has radius 5 cm and height 8 cm. The cone has the same radius and slant height 13 cm. Find the total volume and total curved surface area.

Step 1: Volume of cylinder = πr²h = (22/7) × 5² × 8 Step 2: = (22/7) × 25 × 8 = (22/7) × 200 Step 3: = 4400/7 ≈ 628.57 cm³ Step 4: For cone, slant height l = 13 cm, radius r = 5 cm Step 5: Height of cone: h² = l² − r² = 13² − 5² = 169 − 25 = 144 Step 6: h = 12 cm Step 7: Volume of cone = (1/3)πr²h =...

Q3: Find the volume of a frustum of a cone if the radii of the two circular ends are 5 cm and 3 cm, and the height is 6 cm. (Use π = 22/7)

Step 1: Volume of frustum = (1/3)πh(R² + r² + Rr) Step 2: Here, R = 5 cm (larger radius), r = 3 cm (smaller radius), h = 6 cm Step 3: Volume = (1/3) × (22/7) × 6 × (5² + 3² + 5×3) Step 4: Volume = (1/3) × (22/7) × 6 × (25 + 9 + 15) Step 5: Volume = (1/3) × (22/7) × 6 × 49 Step 6: Volume = (22/7) × 2...

Showing 3 of 9 questions. Visit the full page for complete solutions.