Question

Find the volume, lateral surface area and the total surface area of a cube each of whose 14c edges measures:

(i) 7 m

(ii) 5.6 cm

(iii) 8 dm 5 cm

Answer 1

(i)Edge of cube (a)=7 m

(a)Volume $=a^3=(7{)}^3=7\times 7\times 7m^3$

$=343m^3$

(b)Lateral surface area $=4a^2$

$=4(7{)}^2=4\times 49m^2=196m^2$

(c)Total surface area $=6a^2=6(7{)}^2{m}^2$

$=6\times 49=294m^2$

(ii)Edge of cube (a)=5.6 cm.

(a)Volume $=a^3=(5.6{)}^{3}c{m}^3$

$=5.6\times 5.6\times 5.6c{m}^2=175.616c{m}^3$

(b)Lateral surface area $=4a^2$

$=4(5.6{)}^2=4\times 5.6\times 5.6cm62$

$=125.44c{m}^2$

(c) Total surface area $=6a^2=6\times (5.6{)}^{2}c{m}^2$

$=6\times 5.6\times 5.6c{m}^2=188.16c{m}^2$

(iii)Edge of cube (a)=8 dm 5 cm =85 cm.

(a)Volume $=a^3=(85{)}^{3}c{m}^3$

$=85\times 85\times 85=614125c{m}^3$

(b)Lateral surface area $=4a^2$

$=4\times (85{)}^{2}c{m}^2$

$=4\times 85\times 85=43350c{m}^2$