Advertisements
Advertisements
प्रश्न
In a shopping mall there is a hall of cuboid shape with dimension 800 × 800 × 720 units, which needs to be added the facility of an escalator in the path as shown by the dotted line in the figure. Find the minimum total length of the escalator
Advertisements
उत्तर
Give the dimension of the cube = 800 × 800 × 720
Minimum total length of the escalator:
Shape of the hall is cuboid
The path of the escalator is
From OA to AB to BC to CD
OE = 800
EA = `1/4 xx "Height of the building"`
EA = `1/4 xx 720` = 180
Since there are four steps for the escalator
∴ OA2 = OE2 + EA2
= 8002 + 1802
= (40 × 20)2 + (9 × 20)2
= 402 × 202 + 92 × 202
= 202 (402 + 92)
= 202 (1600 + 81)
= 202 × 1681
OA2 = 202 × 412
OA = `sqrt(20^2 xx 41^2)`
= 20 × 41
= 820
Since ∆OAE ≡ ∆ABB’ ≡ ∆ BCC ≡ ∆CDD’
We have OA = AB = BC = CD
Total length of the escalator
= OA + AB + BC + CD
= 820 + 820 + 820 + 820
= 4 × 820
= 3280
Minimum length of the escalator = 3280 units
APPEARS IN
संबंधित प्रश्न
Find the slope of the following line which passes through the points:
A(2, −1), B(4, 3)
A line makes intercepts 3 and 3 on the co-ordinate axes. Find the inclination of the line.
A line passes through points A(x1, y1) and B(h, k). If the slope of the line is m then show that k − y1 = m(h − x1)
If points A(h, 0), B(0, k) and C(a, b) lie on a line then show that `"a"/"h" + "b"/"k"` = 1
Select the correct option from the given alternatives:
If kx + 2y − 1 = 0 and 6x − 4y + 2 = 0 are identical lines, then determine k
Answer the following question:
Find the value of k if the slope of the line passing through the points P(3, 4), Q(5, k) is 9
Find the equation of the lines passing through the point (1, 1) with y-intercept (– 4)
Find the equation of the lines passing through the point (1, 1) and the perpendicular from the origin makes an angle 60° with x-axis
The normal boiling point of water is 100°C or 212°F and the freezing point of water is 0°C or 32°F. Find the value of C for 98.6°F
The normal boiling point of water is 100°C or 212°F and the freezing point of water is 0°C or 32°F. Find the value of F for 38°C
An object was launched from a place P in constant speed to hit a target. At the 15th second, it was 1400 m from the target, and at the 18th second 800 m away. Find time taken to hit the target
Find the equation of the straight lines passing through (8, 3) and having intercepts whose sum is 1
A straight line is passing through the point A(1, 2) with slope `5/12`. Find points on the line which are 13 units away from A
A spring was hung from a hook in the ceiling. A number of different weights were attached to the spring to make it stretch, and the total length of the spring was measured each time is shown in the following table
| Weight (kg) | 2 | 4 | 5 | 8 |
| Length (cm) | 3 | 4 | 4.5 | 6 |
What is the actual length of the spring
A spring was hung from a hook in the ceiling. A number of different weights were attached to the spring to make it stretch, and the total length of the spring was measured each time is shown in the following table
| Weight (kg) | 2 | 4 | 5 | 8 |
| Length (cm) | 3 | 4 | 4.5 | 6 |
If the spring has to stretch to 9 cm long, how much weight should be added?
A family is using Liquefied petroleum gas (LPG) of weight 14.2 kg for consumption. (Full weight 29.5kg includes the empty cylinders tare weight of 15.3kg.). If it is used with constant rate then it lasts for 24 days. Then the new cylinder is replaced. Draw the graph for first 96days
In a shopping mall there is a hall of cuboid shape with dimension 800 × 800 × 720 units, which needs to be added the facility of an escalator in the path as shown by the dotted line in the figure. Find the heights at which the escalator changes its direction
Choose the correct alternative:
The line (p + 2q)x + (p − 3q)y = p − q for different values of p and q passes through the point
The number of possible tangents which can be drawn to the curve 4x2 – 9y2 = 36, which are perpendicular to the straight line 5x + 2y – 10 = 0 is ______.
