Calculating Storage Box Volume
The storage box is a right rectangular prism. To find how many liters it can hold, we first calculate its internal volume in cubic centimeters (cm³). The formula for the volume (V) of a rectangular prism is:
$ V = \text{length} \times \text{width} \times \text{height} $
Determining Volume in Cubic Centimeters
Given the internal dimensions:
- Length = 50 cm
- Width = 40 cm
- Height = 30 cm
Substitute these values into the volume formula:
$ V = 50 \, \text{cm} \times 40 \, \text{cm} \times 30 \, \text{cm} $
$ V = 2000 \, \text{cm}^2 \times 30 \, \text{cm} $
$ V = 60,000 \, \text{cm}^3 $
Converting Volume to Liters
We need to convert the volume from cubic centimeters (cm³) to liters (L). The conversion factor is:
$ 1 \, \text{L} = 1000 \, \text{cm}^3 $
To find the volume in liters, divide the volume in cm³ by 1000:
$ \text{Volume in Liters} = \frac{V \, (\text{cm}^3)}{1000 \, (\text{cm}^3/\text{L})} $
$ \text{Volume in Liters} = \frac{60,000 \, \text{cm}^3}{1000 \, \text{cm}^3/\text{L}} $
$ \text{Volume in Liters} = 60 \, \text{L} $
Therefore, the storage box can hold 60 liters.
Similar Questions
- The base area of a prism is increased by 25%, while the height remains the same. By what percentage does the volume increase?
- A pyramid with an equilateral triangular base of side 10 cm and height 14 cm is placed on top of a cube with side length 10 cm. Find the total volume of the composite solid.
- In a right prism with a square base, volume = $1024 \text{ cm}^3$ and height = 16 cm. What is the side of the square base?
- If the numerical value of the volume of a sphere is equal to the numerical value of its surface area, find the radius of the sphere.
- A water tank is shaped like a composite prism: the bottom part is a triangular prism with base area 60 cm² and height 1.2 m, while the top part is a rectangular prism with base 40 cm × 30 cm and height 0.8 m. What is the total volume of the tank in liters? (1 m³ = 1000 L)
- A company designs a new chocolate box in the shape of a regular right pyramid with a square base. The base side of the box is 10 cm and its height is 12 cm. Due to packaging constraints, the box can only be filled up to 90% of its total volume. If the company wants to estimate the total cost of chocolate, knowing that $1 \text{ cm}^3$ of chocolate costs ₹0.50, what is the cost of chocolate to fill one such box?
- A right prism has a base in the shape of a trapezium with parallel sides 10 cm and 6 cm, and height 4 cm. If the prism height is 15 cm, what is the volume?
- A pyramid is inscribed inside a cube with edge 12 cm, sharing the base and apex at center of top. Find volume of pyramid.
- A spherical balloon is inflated causing its radius to grow by 10%. By what percentage does its surface area increase?
- A bucket can hold 6.25 liters of water. How many such buckets are needed to fill a 1 cubic meter tank?
Important Questions from 3-D Mensuration
- Find the surface area of a sphere whose diameter is equal to 98 cm.
- A conical vessel has base radius 31 cm and height 45 cm. Water is poured into the vessel until it is $\frac{2}{3}$ full. Find the volume (in cm³) of water in the vessel.
- A solid metallic sphere of radius 10 cm is melted and recast into 125 identical spheres. What is the ratio of the surface area of the original sphere to the total surface area of 6 smaller spheres so formed?
- Find the volume (in cm³) of the largest right circular cone that can be cut out from a cube with an edge of 8 cm. Use $\pi = \frac{22}{7}$
- The volume of a solid cylinder is 5852 cm³ and its height is 38 cm. What is the total surface area of the solid cylinder? (Round your answer to the nearest integer) (Use $\pi = \frac{22}{7}$)
