A right triangular prism has a right-angled triangular base with legs 10 cm and 12 cm, and height 20 cm. If the material density is 6 g/cm^3, find the weight (in kg) of the prism.
Aptitude
Volume and Surface Area
Difficulty: Easy
Choose an option
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A7.2 kg
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B6.4 kg
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C4.8 kg
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D3.4 kg
Answer
Correct Answer: 7.2 kg
Explanation
Introduction / Context:The mass of a solid is density times volume. For a right prism, volume equals the area of its base multiplied by its height (length).
Given Data / Assumptions:
- Right triangle legs: 10 cm and 12 cm.
- Prism height (length): 20 cm.
- Density: 6 g/cm^3.
Concept / Approach:Compute base area A = (1/2)*a*b, then volume V = A*height. Convert grams to kilograms at the end (1000 g = 1 kg).
Step-by-Step Solution:
A = (1/2) * 10 * 12 = 60 cm^2V = 60 * 20 = 1200 cm^3Mass = density * volume = 6 * 1200 = 7200 g = 7.2 kgVerification / Alternative check:Units: (g/cm^3)*(cm^3) = g → convert to kg by dividing by 1000.
Why Other Options Are Wrong:6.4, 4.8, 3.4 kg are off the exact density-volume product.
Common Pitfalls:Using hypotenuse instead of legs; forgetting the 1/2 in the triangular area; missing unit conversion to kg.
Final Answer:7.2 kg