1. **Problem statement:** Calculate perimeter and area of various shapes, volumes, and paint coverage as described. 2. Circle with diameter 23 feet: - Radius $r=\frac{23}{2}=11.5$ ft - Area $=\pi r^2=\pi \times 11.5^2=\pi \times 132.25=415.48$ ft$^2$ - Circumference $=2\pi r=2\pi \times 11.5=72.26$ ft 3. Square with sides 1.4 cm: - Perimeter $=4 \times 1.4=5.6$ cm - Area $=1.4^2=1.96$ cm$^2$ 4. Rectangular postage stamp 2.2 cm by 1 cm: - Perimeter $=2(2.2+1)=6.4$ cm - Area $=2.2 \times 1=2.2$ cm$^2$ 5. Parallelogram with sides 4.5 ft and 12.2 ft, height = 3.6 ft: - Perimeter $=2(4.5+12.2)=33.4$ ft - Area $=\text{base} \times \text{height}=12.2 \times 3.6=43.92$ ft$^2$ 6. Square state park with sides 6 miles: - Perimeter $=4 \times 6=24$ miles - Area $=6^2=36$ miles$^2$ 7. Rectangular envelope 8 in by 14 in: - Perimeter $=2(8+14)=44$ in - Area $=8 \times 14=112$ in$^2$ 8. Parallelogram sides 8 ft and 30 ft, height 4 ft: - Perimeter $=2(8+30)=76$ ft - Area $=30 \times 4=120$ ft$^2$ 9. Swimming pool (rectangular prism): 50 m long, 30 m wide, 2.5 m deep: - Volume $=50 \times 30 \times 2.5=3750$ m$^3$ 10. Arena floor 40 m by 50 m, ceiling 8 m high: - Volume $=40 \times 50 \times 8=16000$ m$^3$ - Volume in liters $=16000 \times 1000=16000000$ L 11. Air duct circular cross-section radius 18 in (1.5 ft), length 40 ft: - Radius $r=\frac{18}{12}=1.5$ ft - Volume of cylinder $=\pi r^2 h=\pi \times 1.5^2 \times 40=\pi \times 2.25 \times 40=282.74$ ft$^3$ - Surface area of side $=2\pi r h=2\pi \times 1.5 \times 40=376.99$ ft$^2$ - Paint needed equals lateral surface area $=376.99$ ft$^2$ 12. Grain storage hemispherical shell radius 30 m: - Volume hemisphere $=\frac{2}{3}\pi r^3=\frac{2}{3}\pi \times 30^3=\frac{2}{3}\pi \times 27000=56548.67$ m$^3$ - Surface area hemisphere (excluding base) $=2\pi r^2=2\pi \times 30^2=5654.87$ m$^2$ - Paint needed $=5654.87$ m$^2$ 13. Tennis balls stacked in cylindrical can: - Diameter of one ball = $d$, height of can = $3d$ - Circumference $=\pi d$ vs height $=3d$ - Since $3d > \pi d$ (approximately 3 > 3.14? No, actually $3 < 3.14$) - Circumference $=3.14d$ is greater than height $=3d$ Final answers summarized.