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The volume of a cuboid is twice that of a cube . If the dimensions of the cuboid are 9 cm, 8 cm and 6 cm, the total surface area of the cube is :
Answer & Solution
Correct Answer:
Option
C
Volume of the cuboid :
$$\eqalign{ & = \left( {9 \times 8 \times 6} \right){\text{ c}}{{\text{m}}^3} \cr & = 432{\text{ c}}{{\text{m}}^3} \cr} $$
Volume of the cube :
$$\eqalign{ & = \left( {\frac{1}{2} \times 432} \right){\text{ c}}{{\text{m}}^3} \cr & = 216{\text{ c}}{{\text{m}}^3} \cr} $$
$$\eqalign{ & {a^3} = 216 \cr & a = \root 3 \of {216} \cr & a = 6 \cr & 6{a^2} = 6 \times {6^2} \cr & 6{a^2} = 216 \text{ cm}^2 \cr} $$
$$\eqalign{ & = \left( {9 \times 8 \times 6} \right){\text{ c}}{{\text{m}}^3} \cr & = 432{\text{ c}}{{\text{m}}^3} \cr} $$
Volume of the cube :
$$\eqalign{ & = \left( {\frac{1}{2} \times 432} \right){\text{ c}}{{\text{m}}^3} \cr & = 216{\text{ c}}{{\text{m}}^3} \cr} $$
$$\eqalign{ & {a^3} = 216 \cr & a = \root 3 \of {216} \cr & a = 6 \cr & 6{a^2} = 6 \times {6^2} \cr & 6{a^2} = 216 \text{ cm}^2 \cr} $$
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