Calculating Square Areas
First, find the area of the original large square.
- Side of the large square = $10 \text{ cm}$
- Original Area = Side $\times$ Side = $10 \text{ cm} \times 10 \text{ cm} = 100 \text{ cm}^2$
Determining Removed Area
Next, calculate the area of the smaller square that was removed.
- Side of the small square = $4 \text{ cm}$
- Removed Area = Side $\times$ Side = $4 \text{ cm} \times 4 \text{ cm} = 16 \text{ cm}^2$
Finding the Remaining Area
Subtract the removed area from the original area to find the remaining area.
- Remaining Area = Original Area - Removed Area
- Remaining Area = $100 \text{ cm}^2 - 16 \text{ cm}^2 = 84 \text{ cm}^2$
Calculating the Ratio
Finally, determine the ratio of the remaining area to the original area and simplify it.
- Ratio = Remaining Area : Original Area
- Ratio = $84 : 100$
- Simplify the ratio by dividing both numbers by their greatest common divisor (4):
- Simplified Ratio = $\frac{84}{4} : \frac{100}{4} = 21 : 25$
The ratio of the remaining area to the original area is 21:25.
Similar Questions
- A solid pyramid is to be painted. If paint covers 2 $m^2$/litre and total surface is 48 $m^2$, how much paint is needed, including 5% extra for retouch?
- A sphere is inscribed inside a cube. The volume of the cube is $1728\text{ cm}^3$. What is the total surface area of the sphere?
- A large wooden box, open at the top, needs to be lined with fabric on its inner floor and inner four side walls. The inner dimensions of the box are 2.5 m length, 1.8 m wide, and 1.2 m high. If the fabric comes in square pieces of side 50 cm, and 15% extra fabric is needed for cuts and overlaps, how many approximate fabric pieces should be purchased?
- A rectangular park is 60 m by 40 m. A semicircular pond of diameter 40 m is inside. What percent of the park's area does the pond occupy?
- A regular hexagon has a perimeter of 72 cm. What is its area?
- A triangular prism has a base with area 45 $\text{cm}^2$ and height 14 cm. If 10% of the prism is hollowed out for wiring, what is the volume of the solid part?
- A circular jogging track has a radius of 50 m. A runner covers a curved path that subtends an angle of $120^\circ$ at the center. What is the length of the arc she runs?
- What is the area of the segment formed by a chord in a circle of radius 6 cm, if the angle subtended at the center is $120^{\circ}$?
- What is the area of the segment formed by a chord in a circle of radius $10\text{ cm}$, if the angle subtended at the center is $90^\circ$?
The angle of a sector is π/4 radians, and the radius of the circle is 8 cm. What is the area of the sector?
Important Questions from Mensuration
In a circular garden of radius 15 m, a path of 2 m wide has to be made inside the garden at the rate of ₹ 24 per sq. m. The cost of making the path is: (Take π = \(\frac{22}{7}\) )
A hollow cylinder with outer radius 4 cm and height 2 cm is made up of 1 cm thick metal sheet. What is the volume of metal used? (Take π = \(\frac{22}{7}\))
The length and breadth of a rectangular field are in the ratio 4 : 3. If the cost of cultivating the field at ₹2 per m 2is ₹600, then the length of the field is:
A cylindrical tank has a capacity of 5632 m3. If the diameter of its base is 8 m, what is the depth of the cylindrical tank? (Use π = \(\frac{22}{7}\))
Find the surface area of a sphere whose diameter is equal to 28 cm.
