Pyramid Volume Calculation
The problem asks for the cost to fill 90% of a chocolate box shaped like a regular right pyramid with a square base.
- Given: Base side length, $s = 10$ cm; Height, $h = 12$ cm; Fill percentage = 90%; Cost = ₹0.50 per $cm^3$.
- First, calculate the area of the square base ($A$):
$A = s^2 = (10 \text{ cm})^2 = 100 \text{ cm}^2$
- Next, calculate the total volume ($V$) of the pyramid using the formula:
$V = \frac{1}{3} \times \text{Base Area} \times \text{Height}$
$V = \frac{1}{3} \times 100 \text{ cm}^2 \times 12 \text{ cm} = \frac{1200}{3} \text{ cm}^3 = 400 \text{ cm}^3$
- Calculate the volume needed for filling (90% of total volume):
$V_{fill} = 0.90 \times V = 0.90 \times 400 \text{ cm}^3 = 360 \text{ cm}^3$
Chocolate Cost Estimation
Finally, calculate the total cost based on the volume to be filled and the cost per cubic centimeter.
- Total Cost = Volume to fill $\times$ Cost per $cm^3$
$ \text{Cost} = 360 \text{ cm}^3 \times \text{₹}0.50/\text{cm}^3 = \text{₹}180 $
The cost of chocolate to fill one such box up to 90% capacity is ₹180.
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 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 storage box is in the shape of a right rectangular prism with internal dimensions 50 cm $\times$ 40 cm $\times$ 30 cm. How many liters can it hold?
- 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 $\pi = \frac{22}{7}$)
