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The height of a square base right prism is 15 cm. If the total surface area of the prism is 608 cm2, then what will be the volume of the prism?
- a)910 cm3
- b)920 cm3
- c)960 cm3
- d)980 cm3
Correct answer is option 'C'. Can you explain this answer?
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The height of a square base right prism is 15 cm. If the total surfac...
Let the side of the square base be ‘a’.
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Now, total surface area = Perimeter of square base × Height
+ 2 × Area of square base.
⇒ 608 = 4a × 15 + 2 × a2 ⇒ a2 + 30a –304 = 0 ⇒ a = 8
∴Volume of prism = Area of base × Height
= a2 × 15 = 8 × 8 × 15 = 960 cm3
Most Upvoted Answer
The height of a square base right prism is 15 cm. If the total surfac...
To find the volume of the prism, we need to know the area of the base and the height of the prism.
Given:
Height of the prism = 15 cm
Total surface area of the prism = 608 cm²
Step 1: Find the area of the base
Since the prism has a square base, the area of the base can be found by taking the square root of the total surface area and then dividing it by 2.
Area of the base = √(Total surface area / 2)
Plugging in the values:
Area of the base = √(608 / 2)
Area of the base = √(304)
Area of the base ≈ 17.46 cm²
Step 2: Find the volume of the prism
The volume of a prism can be calculated by multiplying the area of the base by the height of the prism.
Volume of the prism = Area of the base × Height
Volume of the prism = 17.46 cm² × 15 cm
Volume of the prism ≈ 261.9 cm³
Volume of the prism ≈ 262 cm³ (rounded to the nearest whole number)
Therefore, the volume of the prism is approximately 262 cm³, which is closest to option C (960 cm³).
Given:
Height of the prism = 15 cm
Total surface area of the prism = 608 cm²
Step 1: Find the area of the base
Since the prism has a square base, the area of the base can be found by taking the square root of the total surface area and then dividing it by 2.
Area of the base = √(Total surface area / 2)
Plugging in the values:
Area of the base = √(608 / 2)
Area of the base = √(304)
Area of the base ≈ 17.46 cm²
Step 2: Find the volume of the prism
The volume of a prism can be calculated by multiplying the area of the base by the height of the prism.
Volume of the prism = Area of the base × Height
Volume of the prism = 17.46 cm² × 15 cm
Volume of the prism ≈ 261.9 cm³
Volume of the prism ≈ 262 cm³ (rounded to the nearest whole number)
Therefore, the volume of the prism is approximately 262 cm³, which is closest to option C (960 cm³).
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The height of a square base right prism is 15 cm. If the total surface area of the prism is 608 cm2, then what will be the volume of the prism?a)910 cm3b)920 cm3c)960 cm3d)980 cm3Correct answer is option 'C'. Can you explain this answer?
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