The radius of a sphere is 10 cm. Find its surface area and volume. 2. The diameter of an iron ball is 6 cm. Find its surface area and volume (use pi = 3.14).

Question

Asked on May 9, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

Accepted Answer · 2026-05-09T11:08:05.878Z

9: 1. The radius of a sphere is 10 cm. Find its surface area and volume. Step 1: Identify the given radius and the formulas for surface area and volume of a sphere. Given: r = 10 cm. Surface Area (SA) = 4 r^2 Volume (V) = (4)/(3) r^3 Step 2: Calculate the surface area. SA = 4 (10 cm)^2 SA = 4 (100 cm^2) SA = 400 cm^2 Using ≈ 3.14159: SA ≈ 400 × 3.14159 cm^2 SA ≈ 1256.64 cm^2 Step 3: Calculate the volume. V = (4)/(3) (10 cm)^3 V = (4)/(3) (1000 cm^3) V = (4000)/(3) cm^3 Using ≈ 3.14159: V ≈ (4000)/(3) × 3.14159 cm^3 V ≈ 1333.33 × 3.14159 cm^3 V ≈ 4188.79 cm^3 The surface area is 400 cm^2 or approximately 1256.64 cm^2 and the volume is (4000)/(3) cm^3 or approximately 4188.79 cm^3. 2. The diameter of an iron ball is 6 cm. Find its surface area and volume (use = 3.14). Step 1: Identify the given diameter and calculate the radius. Given: d = 6 cm. Radius r = (d)/(2) = 6 cm2 = 3 cm. Use = 3.14. Step 2: Calculate the surface area. SA = 4 r^2 SA = 4 × 3.14 × (3 cm)^2 SA = 4 × 3.14 × 9 cm^2 SA = 12.56 × 9 cm^2 SA = 113.04 cm^2 Step 3: Calculate the volume. V = (4)/(3) r^3 V = (4)/(3) × 3.14 × (3 cm)^3 V = (4)/(3) × 3.14 × 27 cm^3 V = 4 × 3.14 × 9 cm^3 V = 113.04 cm^3 The surface area is 113.04 cm^2 and the volume is 113.04 cm^3. 3. Find the formula for the surface area and volume of a sphere in terms of its diameter d. Step 1: Relate the radius (r) to the diameter (d). r = (d)/(2) Step 2: Substitute r = (d)/(2) into the surface area formula (SA = 4 r^2). SA = 4 ((d)/(2))^2 SA = 4 ((d^2)/(4)) SA = d^2 The formula for surface area in terms of diameter is SA = d^2. Step 3: Substitute r = (d)/(2) into the volume formula (V = (4)/(3) r^3). V = (4)/(3) ((d)/(2))^3 V = (4)/(3) ((d^3)/(8)) V = (4 d^3)/(24) V = (1)/(6) d^3 The formula for volume in terms of diameter is V = (1)/(6) d^3. 3 done, 2 left today. You're making progress.

Accepted Answer · 2026-05-09T11:08:05.878Z

9: 1. The radius of a sphere is 10 cm. Find its surface area and volume. Step 1: Identify the given radius and the formulas for surface area and volume of a sphere. Given: r = 10 cm. Surface Area (SA) = 4 r^2 Volume (V) = (4)/(3) r^3 Step 2: Calculate the surface area. SA = 4 (10 cm)^2 SA = 4 (100 cm^2) SA = 400 cm^2 Using ≈ 3.14159: SA ≈ 400 × 3.14159 cm^2 SA ≈ 1256.64 cm^2 Step 3: Calculate the volume. V = (4)/(3) (10 cm)^3 V = (4)/(3) (1000 cm^3) V = (4000)/(3) cm^3 Using ≈ 3.14159: V ≈ (4000)/(3) × 3.14159 cm^3 V ≈ 1333.33 × 3.14159 cm^3 V ≈ 4188.79 cm^3 The surface area is 400 cm^2 or approximately 1256.64 cm^2 and the volume is (4000)/(3) cm^3 or approximately 4188.79 cm^3. 2. The diameter of an iron ball is 6 cm. Find its surface area and volume (use = 3.14). Step 1: Identify the given diameter and calculate the radius. Given: d = 6 cm. Radius r = (d)/(2) = 6 cm2 = 3 cm. Use = 3.14. Step 2: Calculate the surface area. SA = 4 r^2 SA = 4 × 3.14 × (3 cm)^2 SA = 4 × 3.14 × 9 cm^2 SA = 12.56 × 9 cm^2 SA = 113.04 cm^2 Step 3: Calculate the volume. V = (4)/(3) r^3 V = (4)/(3) × 3.14 × (3 cm)^3 V = (4)/(3) × 3.14 × 27 cm^3 V = 4 × 3.14 × 9 cm^3 V = 113.04 cm^3 The surface area is 113.04 cm^2 and the volume is 113.04 cm^3. 3. Find the formula for the surface area and volume of a sphere in terms of its diameter d. Step 1: Relate the radius (r) to the diameter (d). r = (d)/(2) Step 2: Substitute r = (d)/(2) into the surface area formula (SA = 4 r^2). SA = 4 ((d)/(2))^2 SA = 4 ((d^2)/(4)) SA = d^2 The formula for surface area in terms of diameter is SA = d^2. Step 3: Substitute r = (d)/(2) into the volume formula (V = (4)/(3) r^3). V = (4)/(3) ((d)/(2))^3 V = (4)/(3) ((d^3)/(8)) V = (4 d^3)/(24) V = (1)/(6) d^3 The formula for volume in terms of diameter is V = (1)/(6) d^3. 3 done, 2 left today. You're making progress.

The radius of a sphere is 10 cm. Find its surface area and volume. 2. The diameter of an iron ball is 6 cm. Find its surface area and volume (use pi = 3.14).

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The radius of a sphere is 10 cm. Find its surface area and volume. 2. The diameter of an iron ball is 6 cm. Find its surface area and volume (use pi = 3.14).

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