To find the combined area of both bases of the prism, we first need to calculate the Lateral Surface Area (LSA) and then use the formula for Total Surface Area (TSA).
Calculating Lateral Surface Area (LSA)
The Lateral Surface Area of a prism is calculated by multiplying the perimeter of the base by the height of the prism.
- Base Perimeter ($P$) = 30 cm
- Height ($h$) = 7 cm
- The formula for LSA is:
$LSA = P \times h$
- Substituting the values:
$LSA = 30 \text{ cm} \times 7 \text{ cm} = 210 \text{ cm}^2$
Calculating Combined Base Area
The Total Surface Area (TSA) of a prism is the sum of the Lateral Surface Area (LSA) and the area of both bases (2 $\times$ Base Area).
- Total Surface Area ($TSA$) = 282 cm$^2$
- Lateral Surface Area ($LSA$) = 210 cm$^2$
- Let the area of both bases combined be $2B$.
- The formula for TSA is:
$TSA = LSA + 2B$
- We need to find $2B$. Rearranging the formula:
$2B = TSA - LSA$
- Substituting the values:
$2B = 282 \text{ cm}^2 - 210 \text{ cm}^2$
- Therefore, the combined area of both bases is:
$2B = 72 \text{ cm}^2$
The area of both bases combined is 72 cm$^2$.
Similar Questions
A right circular cone having height of 30 cm is cut by two parallel planes at heights 10 cm and 20 cm from the base. What is the ratio of the volumes of the three parts (from top to bottom)?
Two hemispheres of radii 2 cm and 4 cm respectively are melted and recast into another hemisphere. What is the approximate total surface area of the newly formed hemisphere?
A solid cylinder has a radius of 5 cm and a height of 10 cm. A smaller cylindrical hole of radius 3 cm is drilled coaxially through its entire length. What is the approximate volume of the remaining solid?
A prism has an equilateral triangular base with a side length of 4 cm. Its height starts at 5 cm and increases by 1 cm for each subsequent layer, forming 5 layers in total. What is the total volume of the prism? (Use \(\sqrt{3} \approx 1.732\))
A solid sphere is placed inside a cube such that it touches all six faces. What percentage of the cube's volume is not occupied by the sphere?
A sphere is completely contained within a cylinder, with the height and diameter of the cylinder matching the diameter of the sphere. Given that the volume of the sphere is 36π cm³, what is the volume of the vacant space inside the cylinder?
Two solid hemispheres of radii 6 cm and 8 cm respectively are melted and recast into a single hemisphere. What is the approximate radius of the new hemisphere formed?
A regular right pyramid has a square base with a side length of 12 cm. Its slant height is 10 cm. What is its volume?
A hemisphere is melted and recast into a cone of the same radius R. Find the height of the cone formed.
A right circular cone has a radius of 7 cm and height of 24 cm. What is the slant height?
Important Questions from 3-D Mensuration
Find the total surface area of a closed cylinder having a base radius of 70 m and a height of 110 m. [Use π = \(22\over7\)]
- The curved surface area of a cylinder is half of its total surface area. If its height is 195 cm, then find its diameter (in cm).
The diameter of the base and slant height of a right circular cone are 30 cm and 113 cm, respectively. Find the volume (in cm³) of the given cone.
(Use $\pi = \frac{22}{7}$)- A cylindrical rod has an curved surface area of $4,900 \text{ cm}^2$. If the length of the rod is 97 cm, then the radius (in cm) of the rod, correct to two places of decimal, is:
Take $\pi = \frac{22}{7}$ - The volume (in $m^3$) of a cube, each of whose edges is 42 m, is:
