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The base of a right pyramid is a regular hexagon whose area is 243 square cm. If the area of a side faces the pyramid is 46 square cm, what should be its volume (in cc) in the nearest integer value?
- a)133.65
- b)138.55
- c)142.55
- d)143.55
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
The base of a right pyramid is a regular hexagon whose area is 243 sq...
Volume of hexagon
= (1/3) × area of base × height
Area of base =243 cm2
⇒6×(√3/4)×a2=243
⇒a2=243×4/6√3=93.53
⇒a=9.67 cm
Area of side force
=(1/2)×a×h=46 cm2
⇒(1/2)×9.67×h=46
⇒h=(46×2)/(9.67)=9.81 cm
Height of prism =
Volume =(1/3)×243×1.65=133.65 cm3
Hence, the correct option is (A).
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The base of a right pyramid is a regular hexagon whose area is 243 sq...
Given Data:
- Area of the regular hexagon base = 243 sq cm
- Area of a side face = 46 sq cm
Calculating the Side Length of the Hexagon Base:
- The formula to find the area of a regular hexagon is A = (3√3)/2 * s^2, where A is the area and s is the side length.
- Given that the area of the hexagon base is 243 sq cm, we can solve for s:
243 = (3√3)/2 * s^2
s^2 = 162/√3
s = √(162/√3)
s ≈ 8.77 cm
Calculating the Height of the Pyramid:
- The height of the pyramid can be calculated using the formula h = √(s^2 - (s/2)^2), where s is the side length of the hexagon base.
- Substituting the value of s, we get:
h = √(8.77^2 - (8.77/2)^2)
h = √(76.84 - 19.21)
h ≈ √57.63
h ≈ 7.59 cm
Calculating the Volume of the Pyramid:
- The volume of a pyramid is given by the formula V = (1/3) * Base Area * Height.
- Substituting the values of the base area and height, we get:
V = (1/3) * 243 * 7.59
V ≈ 133.65 cc
Therefore, the volume of the pyramid is approximately 133.65 cc, which is closest to option A.
- Area of the regular hexagon base = 243 sq cm
- Area of a side face = 46 sq cm
Calculating the Side Length of the Hexagon Base:
- The formula to find the area of a regular hexagon is A = (3√3)/2 * s^2, where A is the area and s is the side length.
- Given that the area of the hexagon base is 243 sq cm, we can solve for s:
243 = (3√3)/2 * s^2
s^2 = 162/√3
s = √(162/√3)
s ≈ 8.77 cm
Calculating the Height of the Pyramid:
- The height of the pyramid can be calculated using the formula h = √(s^2 - (s/2)^2), where s is the side length of the hexagon base.
- Substituting the value of s, we get:
h = √(8.77^2 - (8.77/2)^2)
h = √(76.84 - 19.21)
h ≈ √57.63
h ≈ 7.59 cm
Calculating the Volume of the Pyramid:
- The volume of a pyramid is given by the formula V = (1/3) * Base Area * Height.
- Substituting the values of the base area and height, we get:
V = (1/3) * 243 * 7.59
V ≈ 133.65 cc
Therefore, the volume of the pyramid is approximately 133.65 cc, which is closest to option A.
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The base of a right pyramid is a regular hexagon whose area is 243 square cm. If the area of a side faces the pyramid is 46 square cm, what should be its volume (in cc) in the nearest integer value?a)133.65b)138.55c)142.55d)143.55Correct answer is option 'A'. Can you explain this answer?
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The base of a right pyramid is a regular hexagon whose area is 243 square cm. If the area of a side faces the pyramid is 46 square cm, what should be its volume (in cc) in the nearest integer value?a)133.65b)138.55c)142.55d)143.55Correct answer is option 'A'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about The base of a right pyramid is a regular hexagon whose area is 243 square cm. If the area of a side faces the pyramid is 46 square cm, what should be its volume (in cc) in the nearest integer value?a)133.65b)138.55c)142.55d)143.55Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The base of a right pyramid is a regular hexagon whose area is 243 square cm. If the area of a side faces the pyramid is 46 square cm, what should be its volume (in cc) in the nearest integer value?a)133.65b)138.55c)142.55d)143.55Correct answer is option 'A'. Can you explain this answer?.
The base of a right pyramid is a regular hexagon whose area is 243 square cm. If the area of a side faces the pyramid is 46 square cm, what should be its volume (in cc) in the nearest integer value?a)133.65b)138.55c)142.55d)143.55Correct answer is option 'A'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about The base of a right pyramid is a regular hexagon whose area is 243 square cm. If the area of a side faces the pyramid is 46 square cm, what should be its volume (in cc) in the nearest integer value?a)133.65b)138.55c)142.55d)143.55Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The base of a right pyramid is a regular hexagon whose area is 243 square cm. If the area of a side faces the pyramid is 46 square cm, what should be its volume (in cc) in the nearest integer value?a)133.65b)138.55c)142.55d)143.55Correct answer is option 'A'. Can you explain this answer?.
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