Here are the step-by-step solutions for each problem on the quiz. We will use $\pi \approx 3.14$ and round answers to the nearest tenth as requested.
Formulas used:
*
Cylinder Volume: $V = \pi r^2 h$
*
Cone Volume: $V = \frac{1}{3} \pi r^2 h$
*
Sphere Volume: $V = \frac{4}{3} \pi r^3$
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1. Cylinder
* Diameter = $6\text{ cm}$, so Radius ($r$) = $3\text{ cm}$.
* Height ($h$) = $2.5\text{ cm}$.
* $V = 3.14 \times (3)^2 \times 2.5$
* $V = 3.14 \times 9 \times 2.5$
* $V = 70.65$
* Rounding to nearest tenth:
$70.7\text{ cm}^3$
2. Cylinder
* Radius ($r$) = $8\text{ in}$.
* Height ($h$) = $13\text{ in}$.
* $V = 3.14 \times (8)^2 \times 13$
* $V = 3.14 \times 64 \times 13$
* $V = 2612.48$
* Rounding to nearest tenth:
$2612.5\text{ in}^3$
3. Cylinder
* Diameter = $7\text{ m}$, so Radius ($r$) = $3.5\text{ m}$.
* Height ($h$) = $1\text{ m}$.
* $V = 3.14 \times (3.5)^2 \times 1$
* $V = 3.14 \times 12.25 \times 1$
* $V = 38.465$
* Rounding to nearest tenth:
$38.5\text{ m}^3$
4. Cone
* Diameter = $7\text{ mi}$, so Radius ($r$) = $3.5\text{ mi}$.
* Height ($h$) = $8\text{ mi}$.
* $V = \frac{1}{3} \times 3.14 \times (3.5)^2 \times 8$
* $V = \frac{1}{3} \times 3.14 \times 12.25 \times 8$
* $V = \frac{1}{3} \times 307.72$
* $V \approx 102.57$
* Rounding to nearest tenth:
$102.6\text{ mi}^3$
5. Cone
* Radius ($r$) = $8\text{ cm}$.
* Height ($h$) = $11\text{ cm}$.
* $V = \frac{1}{3} \times 3.14 \times (8)^2 \times 11$
* $V = \frac{1}{3} \times 3.14 \times 64 \times 11$
* $V = \frac{1}{3} \times 2210.56$
* $V \approx 736.85$
* Rounding to nearest tenth:
$736.9\text{ cm}^3$
6. Cone
* Diameter = $14\text{ mm}$, so Radius ($r$) = $7\text{ mm}$.
* Height ($h$) = $12\text{ mm}$.
* $V = \frac{1}{3} \times 3.14 \times (7)^2 \times 12$
* $V = \frac{1}{3} \times 3.14 \times 49 \times 12$
* $V = 3.14 \times 49 \times 4$ *(since $12/3 = 4$)*
* $V = 615.44$
* Rounding to nearest tenth:
$615.4\text{ mm}^3$
7. Sphere
* Diameter = $9\text{ m}$, so Radius ($r$) = $4.5\text{ m}$.
* $V = \frac{4}{3} \times 3.14 \times (4.5)^3$
* $V = 1.333... \times 3.14 \times 91.125$
* $V \approx 381.51$
* Rounding to nearest tenth:
$381.5\text{ m}^3$
8. Sphere
* Radius ($r$) = $4\text{ cm}$.
* $V = \frac{4}{3} \times 3.14 \times (4)^3$
* $V = 1.333... \times 3.14 \times 64$
* $V \approx 267.94$
* Rounding to nearest tenth:
$267.9\text{ cm}^3$
9. Sphere
* Diameter = $12\text{ in}$, so Radius ($r$) = $6\text{ in}$.
* $V = \frac{4}{3} \times 3.14 \times (6)^3$
* $V = 1.333... \times 3.14 \times 216$
* $V = 904.32$
* Rounding to nearest tenth:
$904.3\text{ in}^3$
Final Answer:
1. $70.7\text{ cm}^3$
2. $2612.5\text{ in}^3$
3. $38.5\text{ m}^3$
4. $102.6\text{ mi}^3$
5. $736.9\text{ cm}^3$
6. $615.4\text{ mm}^3$
7. $381.5\text{ m}^3$
8. $267.9\text{ cm}^3$
9. $904.3\text{ in}^3$
Parent Tip: Review the logic above to help your child master the concept of volume of cylinders and cones worksheet.
