15. a cylinder has radius 6 cm and height 14 cm. calculate its volume and total surface area to 3 s.f.
4 marks

section e - scale factor 4 marks
17. a square has side length 5 cm and is enlarged by a scale factor of 3. 4 marks

Question

15. a cylinder has radius 6 cm and height 14 cm. calculate its volume and total surface area to 3 s.f.
4 marks

section e - scale factor 4 marks
17. a square has side length 5 cm and is enlarged by a scale factor of 3. 4 marks

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Significant Figures", "Surface Area and Volume" ], "new_concepts": [ "Scale Factor" ], "current_concepts": [ "Significant Figures", "Surface Area and Volume", "Scale Factor" ] } ## 计算圆柱体的体积 Using the *Surface Area and Volume* knowledge point $$ \begin{aligned} r &= 6\text{ cm},\quad h = 14\text{ cm}\ V &= \pi r^2 h = \pi \times 6^2 \times 14 = 504\pi\text{ cm}^3\ V &\approx 1583.36\text{ cm}^3 \end{aligned} $$ ## 计算圆柱体的总表面积 Using the *Surface Area and Volume* knowledge point $$ \begin{aligned} A &= 2\pi r^2 + 2\pi r h = 2\pi \times 6^2 + 2\pi \times 6 \times 14\ A &= 72\pi + 168\pi = 240\pi\text{ cm}^2\ A &\approx 753.98\text{ cm}^2 \end{aligned} $$ ## 保留三位有效数字 Using the *Significant Figures* knowledge point $$ \begin{aligned} V &\approx 1580\text{ cm}^3 \quad (3\text{ s.f.})\ A &\approx 754\text{ cm}^2 \quad (3\text{ s.f.}) \end{aligned} $$ ## 分析正方形的放大正方形的边长为 $5\text{ cm}$，按比例因子 $3$ 进行放大。放大后的新边长为： $$ 5\text{ cm} \times 3 = 15\text{ cm} $$ ## Question 15 圆柱体的体积和总表面积（保留至 3 位有效数字）分别为： - 体积：$1580\text{ cm}^3$ - 总表面积：$754\text{ cm}^2$ ## Question 17 正方形放大后的新边长为： - 新边长：$15\text{ cm}$ { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Geometry", "Surface Area and Volume" ] }

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QUESTION IMAGE

Question

Explanation:

计算圆柱体的体积

计算圆柱体的总表面积

保留三位有效数字

分析正方形的放大

Answer:

Question 15

Question 17