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Observe the bar graph carefully and answer the given questions: a) What information is given by the bar graph? b) Name the lowest of the given peaks and what is its height. c) Find the ratio of the he

Mathematics

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Here are the solutions to questions 44 to 47.

44. Observe the bar graph carefully and answer the given questions:

From the bar graph, the heights of the mountain peaks are:

  • Kanchenjunga: 8500 m8500 \text{ m}

  • Nanda Devi: 7800 m7800 \text{ m}

  • Mount Everest: 8800 m8800 \text{ m}

  • Himadri: 7800 m7800 \text{ m}

  • Nanga Parbat: 8100 m8100 \text{ m}

  • a) What information is given by the bar graph? The bar graph shows the Heights of Mountain Peaks.

  • b) Name the lowest of the given peaks and what is its height. The lowest height is 7800 m7800 \text{ m}. The lowest peaks are Nanda Devi and Himadri, with a height of 7800 m\boxed{7800 \text{ m}}.

  • c) Find the ratio of the heights of the lowest and highest peaks. Lowest height =7800 m= 7800 \text{ m} Highest height (Mount Everest) =8800 m= 8800 \text{ m} Ratio =Lowest heightHighest height= \frac{\text{Lowest height}}{\text{Highest height}}

    7800 m8800 m=7888=3944\frac{7800 \text{ m}}{8800 \text{ m}} = \frac{78}{88} = \frac{39}{44}

    The ratio is 39:44\boxed{39:44}.

  • d) Write down the measurement of the heights of the peaks in the ascending order. The heights in ascending order are: Himadri (7800 m7800 \text{ m}), Nanda Devi (7800 m7800 \text{ m}), Nanga Parbat (8100 m8100 \text{ m}), Kanchenjunga (8500 m8500 \text{ m}), Mount Everest (8800 m8800 \text{ m}).

45. Charu runs around a square park of sides 85 m85 \text{ m}. Pooja runs around a rectangular park of length 70 m70 \text{ m} and breadth 55 m55 \text{ m}. Who covers less distance?

  1. Calculate the distance covered by Charu.

    Charu runs around a square park with side 85 m85 \text{ m}.
    Distance covered by Charu = Perimeter of square

    PCharu=4×side=4×85 m=340 mP_{\text{Charu}} = 4 \times \text{side} = 4 \times 85 \text{ m} = 340 \text{ m}
  2. Calculate the distance covered by Pooja.

    Pooja runs around a rectangular park with length 70 m70 \text{ m} and breadth 55 m55 \text{ m}.
    Distance covered by Pooja = Perimeter of rectangle

    PPooja=2×(length+breadth)=2×(70 m+55 m)P_{\text{Pooja}} = 2 \times (\text{length} + \text{breadth}) = 2 \times (70 \text{ m} + 55 \text{ m}) PPooja=2×(125 m)=250 mP_{\text{Pooja}} = 2 \times (125 \text{ m}) = 250 \text{ m}
  3. Compare the distances.

    Charu's distance =340 m= 340 \text{ m}
    Pooja's distance =250 m= 250 \text{ m}
    Since 250 m<340 m250 \text{ m} < 340 \text{ m}, Pooja covers less distance.
    Pooja covers less distance.

    46. Diameter of a sphere is 9 cm9 \text{ cm}. What is its radius?

  4. Use the formula relating diameter and radius.

    The radius is half of the diameter.

    Radius=Diameter2\text{Radius} = \frac{\text{Diameter}}{2}
  5. Substitute the given diameter.

    Radius=9 cm2=4.5 cm\text{Radius} = \frac{9 \text{ cm}}{2} = 4.5 \text{ cm}

    The radius is 4.5 cm\boxed{4.5 \text{ cm}}.

    47. How many tiles whose length and breadth are 12 cm12 \text{ cm} and 5 cm5 \text{ cm} respectively will fit in a rectangular region whose length and breadth are 100 cm100 \text{ cm} and 144 cm144 \text{ cm}?

  6. Calculate the area of one tile.

    Length of tile =12 cm= 12 \text{ cm}
    Breadth of tile =5 cm= 5 \text{ cm}
    Area of one tile =12 cm×5 cm=60 cm2= 12 \text{ cm} \times 5 \text{ cm} = 60 \text{ cm}^2

  7. Calculate the area of the rectangular region.

    Length of region =100 cm= 100 \text{ cm}
    Breadth of region =144 cm= 144 \text{ cm}
    Area of rectangular region =100 cm×144 cm=14400 cm2= 100 \text{ cm} \times 144 \text{ cm} = 14400 \text{ cm}^2

  8. Calculate the number of tiles.

    Number of tiles =Area of rectangular regionArea of one tile= \frac{\text{Area of rectangular region}}{\text{Area of one tile}}

    Number of tiles=14400 cm260 cm2=240\text{Number of tiles} = \frac{14400 \text{ cm}^2}{60 \text{ cm}^2} = 240

    The number of tiles is 240\boxed{240}.

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