Question

Which among the following will have the largest value?

• A. Surface area of a cube with side $6\text{cm}$.
• B. Surface area of a cuboid with $l=7\text{cm},b=6\text{cm}$ and $h=5\text{cm}$.
• C. Surface area of the walls of a cube having side $8\text{cm}$.
• D. Surface area of the walls of a cuboid having $l=10\text{cm},b=5\text{cm}$ and $h=6\text{cm}$.

Answer 1

The correct option is C

Surface area of the walls of a cube having side $8\text{cm}$.

We know, $\text{TSA of a cube of side 'a'}=6a^2$
$\text{And, TSA of a cuboid of dimensions}l\times b\times h=2(lb+bh+hl)$

So, surface area of a cube with side $6\text{cm}$
$=6\times (6{)}^2=216{\text{cm}}^2$

Surface area of a cuboid with length $l=7\text{cm},$ breadth $b=6\text{cm}$ and height $h=5\text{cm}$
$=2(lb+bh+hl)$
$=2(7\times 6+6\times 5+5\times 7)$
$=2(42+30+35)$
$=2\times 107=214{\text{cm}}^2$

'To find the surface area of the walls of a three dimensional solid' means 'to find its lateral surface area'.

We know, $\text{LSA of a cube of side 'a'}=4a^2$
$\text{And, LSA of a cuboid of dimensions}l\times b\times h=2(lh+bh)$

So, surface area of the walls of a cube having side $8\text{cm}$
$=4\times (8{)}^2$
$=4\times 64=256{\text{cm}}^2$

Surface area of the walls of a cuboid having length $l=10\text{cm},$ breadth $b=5\text{cm}$ and height $h=6\text{cm}$
$=2(bh+hl)$
$=2(5\times 6+6\times 10)$
$=2(30+60)$
$=2\times 90=180{\text{cm}}^2$

$\therefore$ Surface area of the walls of a cube having side 8 cm has the largest value among the give options.