Question

The TSA of cube is 18 3/8 m. Find its LSA

Answer 1

Step-by-step explanation:

Given surface area of cube =

$18 \frac{3}{8}$

Let us assume side of this cube x

${6x}^{2} = 18 \frac{3}{8} \\ {6x}^{2} = \frac{147}{8} \\ {x}^{2} = \frac{147}{48} \\ {x }^{2} = \frac{49}{16} \\ x = \frac{7}{4} \\ side \: of \: cube \: is \: \frac{7}{4} m \\ volume \: of \: cube \: will \: be \: ( { \frac{7}{4} })^{3} {m}^{2} \\ \: \: \: \: \: \: = \frac{343}{64} {m}^{3} \: ans.$

Answer 2

Step-by-step explanation:

Given:-

The TSA of cube is 18 3/8 m^2

To find:-

Find its LSA

Solution:-

Given that

Total surface Area of a cube = 18 3/8 m^2

=>TSA =[ (18×8)+3]/8 m^2

=>TSA = (144+3)/8

=>TSA = 147/8 m^3

We know that

The total surface area of a cube = 6a^2 sq units

where a is the side of the cube

=>6a^2 = 147/8

=>a^2 =( 147/8)/6

=>a^2 = 147/(8×6)

=>a^2 = 147/48

=>a^2 = 49/16

=>a=√(49/16)

=>a=±7/4

Since the side of the cube cannot be negative

Therefore, a= 7/4

The side of the cube = 7/4 m

Lateral surface area of a cube = 4a^2 sq.units

=>LSA = 4(7/4)^2

=>LSA = (4×7×7)/(4×4)

=>LSA = (7×7)/4

=>LSA = 49/4

=>LSA = 12 1/4 sq.m

Answer:-

Lateral surface area of the given cube is

12 1/4 sq.m

Used formula:-

• total surface area of a cube= 6a^2 sq units
• Lateral surface area of a cube = 4a^2 sq.units