Four identical cones with base diameter of 10 cm are compactly placed inside a box in upright position. What will be the area of square (in cm2) formed by connecting tips of the cones?
100
Cones Arrangement in the Box
The problem describes four identical cones placed compactly inside a box in an upright position. When identical circular bases are placed compactly side-by-side in a square pattern, they form a 2x2 arrangement within the box. Since the cones are upright, their tips are directly above the centers of their bases.
Calculating the Side Length of the Square
We are given that the base diameter of each cone is 10 cm. The radius of the base is half of the diameter.
- Base diameter = 10 cm
- Base radius ($r$) = Diameter / 2 = 10 cm / 2 = 5 cm
When the four cones are placed compactly in a square arrangement, the distance between the centers of the bases of two adjacent cones (either side-by-side in a row or front-to-back in a column) is equal to the sum of their radii. Since the cones are identical, this distance is $r + r = 2r$.
Distance between adjacent base centers = $2 \times 5$ cm = 10 cm.
Since the cones are placed upright, the tips of the cones are vertically aligned with the centers of their bases. Therefore, the horizontal distance between the tip of one cone and the tip of an adjacent cone in the arrangement is the same as the distance between their base centers.
The tips of the four cones form a square. The side length of this square is equal to the distance between the tips of any two adjacent cones.
Side length of the square formed by tips = Distance between adjacent base centers = 10 cm.
Area Calculation
The area of a square is calculated by squaring the length of its side.
Area of square = $(\text{Side length})^2$
Area = $(10 \text{ cm})^2 = 10 \text{ cm} \times 10 \text{ cm} = 100 \text{ cm}^2$
Thus, the area of the square formed by connecting the tips of the cones is 100 cm2.
Important Questions from Numerical Ability
- Arrange in the correct sequence the Percentage method of recipe adjustment.
(i) Determine the total weight of the product needed.
(ii) Calculate the percentage of each ingredient in relation to total weight.
(iii) Convert all ingredients in recipe to gram unit and determine edible portion.
(iv) Check the ratio of ingredients which should be in proper balance.
(v) Multiply each percentage number by the total weight to give exact amount of the ingredient needed.
(vi) Total the weight of ingredients using edible portion.
Choose the correct answer from the code given below : In an examination 10,000 students appeared. The result revealed the number of students who have:
passed in all five subjects = 5583
passed in three subjects only = 1400
passed in two subjects only = 1200
passed in one subject only = 735
failed in English only = 75
failed in Physics only = 145
failed in Chemistry only = 140
failed in Mathematics only = 200
failed in Bio-science only = 157
The number of students passed in at least four subjects is:
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