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Calculate the percentage discount and the area of a circular table top with a diameter of 90 cm, using pi = 3.142.

Mathematics

ScanSolve AI Answer

Answer

5%5\%

6361.05 cm26361.05 \text{ cm}^2

Step-by-step solution

4 steps

26)

  1. Calculate the discount amount.

    The discount is the difference between the marked price and the selling price.

    Discount=Marked Price−Selling PriceDiscount = \text{Marked Price} - \text{Selling Price} Discount=sh. 600−sh. 570Discount = \text{sh. } 600 - \text{sh. } 570 Discount=sh. 30Discount = \text{sh. } 30
  2. Calculate the percentage discount.

    The percentage discount is the discount amount divided by the marked price, multiplied by 100%.

    Percentage Discount=DiscountMarked Price×100%Percentage \text{ } Discount = \frac{Discount}{\text{Marked Price}} \times 100\% Percentage Discount=30 sh.600 sh.×100%Percentage \text{ } Discount = \frac{30 \text{ sh.}}{600 \text{ sh.}} \times 100\% Percentage Discount=120×100%Percentage \text{ } Discount = \frac{1}{20} \times 100\% Percentage Discount=5%Percentage \text{ } Discount = 5\%

    The percentage discount was 5%\boxed{5\%}.

    27)

  3. Determine the radius of the table top.

    The diameter is 90 cm90 \text{ cm}. The radius (rr) is half of the diameter.

    r=Diameter2r = \frac{Diameter}{2} r=90 cm2r = \frac{90 \text{ cm}}{2} r=45 cmr = 45 \text{ cm}
  4. Calculate the area of the table top.

    The area (AA) of a circle is given by the formula A=πr2A = \pi r^2. Use the given value π=3.142\pi = 3.142.

    A=πr2A = \pi r^2 A=3.142×(45 cm)2A = 3.142 \times (45 \text{ cm})^2 A=3.142×2025 cm2A = 3.142 \times 2025 \text{ cm}^2 A=6361.05 cm2A = 6361.05 \text{ cm}^2

    The area of the table top is 6361.05 cm2\boxed{6361.05 \text{ cm}^2}.

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