Subjects geometry

Volume Surface Area A34A45

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1. **Find the volume of a prism** Given formula: $$V = Bh$$ where $B$ is the area of the base and $h$ is the height. Calculate: $$V = 112 \times 23 = 2576$$ 2. **Find the surface area of a prism** Given formula: $$S = Ph + 2B$$ where $P$ is the perimeter of the base, $h$ is the height, and $B$ is the area of the base. Calculate: $$S = 180 \times 23 + 2(112) = 4140 + 224 = 4364$$ 3. **Find the volume of a pyramid** Given formula: $$V = \frac{1}{3} bh$$ where $b$ is the base area and $h$ is the height. Calculate: $$V = \frac{1}{3} (72 \times 7.6) = \frac{1}{3} (547.2) = 182.4$$ 4. **Find the surface area of a pyramid** Given formula: $$S = \frac{1}{2} pl + B$$ where $p$ is the perimeter of the base, $l$ is the slant height, and $B$ is the base area. Note: The problem states "+72" which likely means $B=72$. 5. **Find the volume of a prism** Given formula: $$V = Bh$$ Calculate: $$V = 18 \times 14 = 252$$ 6. **Find the surface area of a cylinder** Given formula: $$S = 2\pi r h + 2\pi r^2$$ but here only lateral surface area is given as $$S = 2\pi r h$$ Calculate: $$S = 2 \pi \times 7 \times 18 \approx 791.7$$ 7. **Given dimensions of a figure:** 9.1 cm, 12 cm, 12 cm (no question stated) 9. **Given dimensions:** 14 in, 9 in (no question stated) Since problems 7 and 9 lack explicit questions, only problems 1 to 6 are solved. Final answers: 1. Volume = 2576 2. Surface Area = 4364 3. Volume = 182.4 4. Surface Area = \frac{1}{2} pl + 72 (incomplete data) 5. Volume = 252 6. Surface Area (lateral) = 791.7