The product of the areas of three adjacent faces of a rectangular box equals___________?
Show answer Hide answer
Answer: C. the square of the volume of the box
Explanation
Letting length, breadth, and height be l, b, and h gives adjacent face areas as lb, bh, and hl. Multiplying these three adjacent face areas together yields the combined product lb squared times bh squared times hl squared. This combined product simplifies algebraically to the square of the volume of the box. Rectangular box faces share common edges forming three distinct adjacent rectangular surface areas. Multiplying terms with identical variables adds their exponents resulting in squared product values. Volume of a rectangular box is defined as the product of its length, breadth, and height.
Geometric property proofs help students understand dimensional relationships in three-dimensional space. Packaging engineers analyze surface area and volume interactions to optimize container manufacturing. Spatial reasoning problems reinforce algebraic exponent rules through geometric shape applications. Option A suggests the volume itself which ignores the exponent squaring resulting from multiplication. Option B suggests twice the volume which misinterprets the algebraic product of surface areas. Option D suggests the cube root of volume which contradicts standard exponential multiplication laws.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
Related questions
Q1. An item's price is cut by 10%. By what percentage must the new price rise to restore its original value_______?
Show answer Hide answer
Answer: C. 11 1/9 %
A ten percent price reduction means the new price stands at ninety percent of the original value. To restore the reduced price back to the original level, the price must increase by ten units relative to the new base. Di...
Q2. What is the probability that a number picked at random from the first 50 natural numbers is composite__________?
Show answer Hide answer
Answer: B. 17/25
Among the first fifty natural numbers, exactly one number is neither prime nor composite. Counting the fifteen prime numbers leaves thirty four composite numbers in the specified range. Dividing thirty four by fifty and...
Q3. A square's perimeter equals a 16 cm by 14 cm rectangle's perimeter. Find the circumference of a semicircle whose diameter equals the square's side (rounded to two decimals)?
Show answer Hide answer
Answer: A. 23.57 cm
The rectangle perimeter is calculated as sixty centimeters, which equals the perimeter of the square. Dividing the square perimeter by four gives a side length of fifteen centimeters for the square. A semicircle with thi...
Q4. Two numbers have a product of 2160 and an HCF of 12. Find the numbers________?
Show answer Hide answer
Answer: A. (36,60)
Let the numbers be represented as twelve x and twelve y based on the given highest common factor of twelve. The product of the numbers is one forty four times x times y, which equals twenty one sixty, making x times y eq...
Q5. A town's population grew from 1,75,000 to 2,62,500 over a decade. What is the average annual percentage increase:________?
Show answer Hide answer
Answer: B. 5%
The population increase of eighty seven thousand five hundred over the base represents a fifty percent total growth. Dividing the total fifty percent growth over the ten year duration yields an average of five percent an...
Q6. An item's price is reduced by 25%. To restore its original price, by what percentage must the new price increase________?
Show answer Hide answer
Answer: A. 33 1/3 %
A twenty five percent price reduction results in a new reduced price equal to seventy five percent of the original. To restore the price back to the original level, a twenty five unit increase is needed on a seventy five...