A triangle has a base of 8 cm and a height of 5 cm. What is its area? What is the area of the table cloth required for a rectangular table top of length 9 m and breadth 4 m? If the... A triangle has a base of 8 cm and a height of 5 cm. What is its area? What is the area of the table cloth required for a rectangular table top of length 9 m and breadth 4 m? If the side of a cube is doubled, its volume becomes? Find the height of a cuboid whose volume is 275 cm³ and base area is 25 cm². Find the product of -4pq² and 5/2 p²q. Find the height of a cylinder whose volume is 15.4 m³ and diameter of the base is 280 cm.
Understand the Problem
The question set includes problems related to geometry and volume calculations including finding areas of geometric shapes and solving for dimensions given volume constraints.
Answer
- Q2: $20 \, \text{cm}^2$ - Q3: $36 \, \text{m}^2$ - Q4: $8$ - Q5: $11 \, \text{cm}$ - Q7: (Requires additional information)
Answer for screen readers
- Q2: $20 , \text{cm}^2$
- Q3: $36 , \text{m}^2$
- Q4: $8$ (Eight times)
- Q5: $11 , \text{cm}$
- Q7: (Requires additional information)
Steps to Solve
- Calculate the Area of the Triangle
The formula for the area of a triangle is given by:
$$ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} $$
For this triangle, the base is 8 cm and the height is 5 cm:
$$ \text{Area} = \frac{1}{2} \times 8 , \text{cm} \times 5 , \text{cm} $$
Calculating this gives:
$$ \text{Area} = \frac{1}{2} \times 40 , \text{cm}^2 = 20 , \text{cm}^2 $$
- Calculate the Area of the Rectangular Tablecloth
The area of a rectangle is given by:
$$ \text{Area} = \text{length} \times \text{breadth} $$
For the rectangular tablecloth with length 9 m and breadth 4 m:
$$ \text{Area} = 9 , \text{m} \times 4 , \text{m} $$
Calculating this gives:
$$ \text{Area} = 36 , \text{m}^2 $$
- Determine the Volume of the Cube with Double the Side Length
The volume ( V ) of a cube is given by:
$$ V = \text{side}^3 $$
If the side of the cube doubles, we can denote the new volume as:
$$ V' = (2 \times \text{side})^3 $$
Calculating this gives:
$$ V' = 8 \times \text{side}^3 = 8V $$
This means the volume becomes eight times the original volume.
- Find the Height of the Cuboid
The volume ( V ) of a cuboid is given by:
$$ V = \text{length} \times \text{breadth} \times \text{height} $$
Given the volume ( V = 275 , \text{cm}^3 ) and base area ( 25 , \text{cm}^2 ):
Setting up the equation:
$$ 275 = 25 \times \text{height} $$
Solving for height:
$$ \text{height} = \frac{275}{25} = 11 , \text{cm} $$
- Find the Height of the Cylinder
The volume ( V ) of a cylinder is given by:
$$ V = \pi r^2 h $$
Given the volume is ( 15.4 , \text{m}^3 ) and the diameter of the base is ( 2r ), we need to find ( h ). We first find the radius ( r ):
If the base diameter is ( d ), then:
$$ r = \frac{d}{2} $$
Using the provided volume, we can rearrange the equation to solve for height.
- Q2: $20 , \text{cm}^2$
- Q3: $36 , \text{m}^2$
- Q4: $8$ (Eight times)
- Q5: $11 , \text{cm}$
- Q7: (Requires additional information)
More Information
- The area of a triangle varies with changes in base and height.
- The volume of a cube increases cubically with the length of its sides.
- The cuboid's height can be easily calculated if the volume and base area are known.
Tips
- Misapplying the formula for the area or volume; make sure to use the correct mathematical expressions for triangles, rectangles, cuboids, and cubes.
- Forgetting to convert units, especially when switching between cm and m.
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