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Calculate the volume of a cylindrical tank with radius 35 cm and height 40 cm, using pi = 22/7. Also, find the marked price of a TV sold for 45,000 after a 10% discount.

Mathematics

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Answers

2 parts
a

50,000/=50,000/=

b

25%25\%

Step-by-step solution

5 steps

Here are the solutions to the problems:

: Volume of a cylindrical tank

Step 1: Identify the given values and formula.
The diameter of the cylindrical tank is 70 cm70 \text{ cm}, so the radius r=702=35 cmr = \frac{70}{2} = 35 \text{ cm}.
The height h=40 cmh = 40 \text{ cm}.
We are given π=227\pi = \frac{22}{7}.
The formula for the volume of a cylinder is V=πr2hV = \pi r^2 h.

Step 2: Substitute the values into the formula.

V=227×(35 cm)2×40 cmV = \frac{22}{7} \times (35 \text{ cm})^2 \times 40 \text{ cm}

Step 3: Calculate the volume.

V=227×1225 cm2×40 cmV = \frac{22}{7} \times 1225 \text{ cm}^2 \times 40 \text{ cm} V=22×12257×40 cm3V = 22 \times \frac{1225}{7} \times 40 \text{ cm}^3 V=22×175×40 cm3V = 22 \times 175 \times 40 \text{ cm}^3 V=22×7000 cm3V = 22 \times 7000 \text{ cm}^3 V=154000 cm3V = 154000 \text{ cm}^3

The volume of the tank is 154000 cm3\boxed{154000 \text{ cm}^3}.

: Marked price and percentage profit of a television

Part a· 2 steps

Find the marked price of the television.

  1. Understand the relationship between selling price, marked price, and discount.

    The shopkeeper sold the television for 45,000/=afterallowinga1045,000/= after allowing a 10% discount. This means the selling price (SP)is90) is 90% of the marked price (MP$).

    SP=MP−(10% of MP)SP = MP - (10\% \text{ of } MP) SP=MP−0.10×MPSP = MP - 0.10 \times MP SP=(1−0.10)×MPSP = (1 - 0.10) \times MP SP=0.90×MPSP = 0.90 \times MP

  2. Substitute the selling price and solve for the marked price.

    45,000=0.90×MP45,000 = 0.90 \times MP MP=45,0000.90MP = \frac{45,000}{0.90} MP=50,000MP = 50,000

    The marked price of the television is 50,000/=\boxed{50,000/=}.

Part b

25%25\%

Calculate his percentage profit if the shopkeeper bought the television at 36,000/=.

  1. Identify the selling price and cost price.

    The selling price (SPSP) is 45,000/=45,000/=.
    The cost price (CPCP) is 36,000/=36,000/=.

  2. Calculate the profit.

    Profit = SP−CPSP - CP
    Profit = 45,000−36,00045,000 - 36,000
    Profit = 9,000/=9,000/=

  3. Calculate the percentage profit.

    Percentage Profit = ProfitCP×100%\frac{\text{Profit}}{CP} \times 100\%
    Percentage Profit = 9,00036,000×100%\frac{9,000}{36,000} \times 100\%
    Percentage Profit = 14×100%\frac{1}{4} \times 100\%
    Percentage Profit = 25%25\%
    The shopkeeper's percentage profit is 25%\boxed{25\%}.

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