Question

Obtain the volume of rectangular boxes with the following length, breadth and height, respectively.
(i) 5a, 3a², 7a⁴
(ii) 2p, 4q, 8r
(iii) xy, 2x²y, 2xy²
(iv) a, 2b, 3c

Answer 1

Volume of rectangle = length x breadth x height. To evaluate volume of rectangular boxes, multiply all the monomials.
(i) \(5a \times 3a^2 \times 7a^4\) 
\(= (5 \times 3 × 7) (a × a^2 × a^4 ) \)
\(= 105a^7\)

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(ii) \( 2p \times 4q \times 8r \)
\(= (2 × 4 × 8 ) (p × q × r ) \)
\(= 64pqr\)

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(iii) \(y \times 2x^2y × 2xy^2\)
 \(=(1 × 2 × 2 )( x × x^2 × x × y × y × y^2 ) \)
\(= 4x^4y^4\)

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(iv) \(a \times 2b \times 3c \)
\(= (1 × 2 × 3 ) (a × b × c)\) 
\(= 6abc\)