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
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- 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?
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- 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
The areas of three adjacent faces of a cuboidal tank are 3 m 2, 12 m 2 and 16 m 2. the capacity of the tank, in litres, is:
Volume of a cuboid is 4800 cm 3. If the height of this cuboid is 20 cm, then what will be the area of the base of cuboid ?
Two similar cubes have heights of 8 cm and 12 cm, respectively. If the capacity of the smaller cube is 80 cm 3, what is the capacity of the bigger cube (in cm 3)?
Three circles of radius 7 cm are kept touching each other. The string is tightly tied around these three circles. What is the length of the string?
Three circles of radius 6 cm are kept touching each other. The string is tightly tied around these three circles. What is the length of the string?
