I'll solve the volume problems for the cylinders, cones, and spheres shown in the quiz. Let me work through each problem one by one.
First, I need to recall the formulas:
- Volume of a cylinder: V = πr²h
- Volume of a cone: V = (1/3)πr²h
- Volume of a sphere: V = (4/3)πr³
Let me start with problem 1 (cylinder):
- Radius r = 6 cm
- Height h = 2.5 cm
- V = π × 6² × 2.5 = π × 36 × 2.5 = 90π ≈ 282.74 cm³
Problem 2 (cylinder):
- Diameter = 8 in, so radius r = 4 in
- Height h = 11 in
- V = π × 4² × 11 = π × 16 × 11 = 176π ≈ 552.92 in³
Problem 3 (cylinder):
- Radius r = 3 cm
- Height h = 4 cm
- V = π × 3² × 4 = π × 9 × 4 = 36π ≈ 113.10 cm³
Problem 4 (cone):
- Radius r = 8 mi
- Height h = 7 mi
- V = (1/3)π × 8² × 7 = (1/3)π × 64 × 7 = (448/3)π ≈ 469.14 mi³
Problem 5 (cone):
- Radius r = 8 in
- Height h = 11 in
- V = (1/3)π × 8² × 11 = (1/3)π × 64 × 11 = (704/3)π ≈ 737.20 in³
Problem 6 (cone):
- Radius r = 12 mm
- Height h = 18 mm
- V = (1/3)π × 12² × 18 = (1/3)π × 144 × 18 = 864π ≈ 2714.34 mm³
Problem 7 (sphere):
- Radius r = 9 in
- V = (4/3)π × 9³ = (4/3)π × 729 = 972π ≈ 3053.63 in³
Problem 8 (sphere):
- Diameter = 4 cm, so radius r = 2 cm
- V = (4/3)π × 2³ = (4/3)π × 8 = (32/3)π ≈ 33.51 cm³
Problem 9 (sphere):
- Radius r = 12 ft
- V = (4/3)π × 12³ = (4/3)π × 1728 = 2304π ≈ 7238.23 ft³
Now I'll provide the final answers rounded to the nearest tenth as requested:
1. 282.7 cm³
2. 552.9 in³
3. 113.1 cm³
4. 469.1 mi³
5. 737.2 in³
6. 2714.3 mm³
7. 3053.6 in³
8. 33.5 cm³
9. 7238.2 ft³
Parent Tip: Review the logic above to help your child master the concept of volume of cylinder and cone worksheet.
