Question

A rectangular box has uniform cross-section with length,breadth and height are 4, 5 and 4 cm, then calculate the volume and surface area of the box.
A. volume=144 \[c{m^3}\] , area =40 \[c{m^2}\]
B. volume=80 \[c{m^3}\] , area =144 \[c{m^2}\]
C. volume=144 \[c{m^3}\], area =80 \[c{m^2}\]
D. volume=24 \[c{m^3}\], area =414 \[c{m^2}\]

Answer 1

Hint:
When we come to know about 3D shapes such as cuboid, cube,cone,sphere,etc we might think about their various surface areas,volume and perimeter. Volume simply means how much space that 3D body can occupy . Surface area means how much area its faces have ,it can be lateral and total surface area. Following are the various formulae surface area and volume of several 3D objects
Cuboid :Total Surface Area=2(lb+bh+lh), Lateral surface Area=2h(l+b), Volume=lbh where l,b and h are the length ,breadth and height of the cuboid.
Cube : Total Surface Area=6 × \[lengt{h^2}\] ,lateral surface area=4 × \[lengt{h^2}\], Volume= \[lengt{h^3}\]
Similarly, we can find surface area and volume of several other shapes.

Complete step by step solution:
Given:Various dimensions of cuboid are,
 Length (l)=4 cm
Breadth (b)=5 cm
Height (h)=4 cm
Volume = lbh=4×5×4= 80 cubic cm

Lateral surface area = 2(l+b) ×h
                  =2(4+5) ×4=2×9×8=144 square cm
Hence ,the answer is OPTION B.
Volume= 80 cubic cm ,Lateral surface area=144 square cm

Note:
For a cuboid the Total Surface Area=2(lb+bh+lh)
Proper care should be taken while conversion of units so that we reach the final answer correctly.