Question

Obtain the volume of rectangular boxes with the following length, breadth and height respectively


(1) 5a, 3a^2,7a^4

(i) 2p, 4p , 8r


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Answer 1

Correct question

Obtain the volume of rectangular boxes with the following length, breadth and height respectively

(1) 5a, 3a^2,7a^4

(i) 2p, 4q , 8r [ or any other variables ]

Given :-

• Length of rectangular boxes

• Breadth of rectangular boxes

• Height of rectangular boxes

To find :-

• Volume

Solution :-

$⟹\: \: \sf\bold{\red{In\: the\: first\: case\: :-}}$

★ As we know ,

Volume of rectangular box = L × B × H

$⟹ \: (5a) \: \times \: ( {3a}^{2} ) \times ( {7a}^{4} )$

$⟹5 \times 3 \times 7 \times a \times {a}^{2} \times {a}^{4}$

★ By using exponential law ,

$⟹15 \times{a}^{1 + 2 + 4} \: \: (\: \: \sf\bold{\blue{When \: bases \: are \: same \: powers \: are \: added}})$

$⟹ {105a}^{7}$

★So therefore volume of rectangular box with

Length = 5a

$Breadth = {3a}^{2}$

$Height = {7a}^{4}$

$is \: \: \sf\bold{\red{ {105a}^{7} }}$

$⟹\: \sf\bold{\orange{In\: the\: second\: case\: :-}}$

★As we know ,

Volume of rectangular box = L × B × H

$⟹ \: 2p \: \times 4q \times 8r$

$⟹2 \times 4 \times 8 \times p \times q \times r$

$⟹64pqr$

★So therefore volume of rectangular box with

Length = 2p

Breadth = 4q

Height = 8r

$is \: \sf\bold{\orange{64pqr}}$

Formula used :-

Volume = L × B × H

Answer 2

105a^7 is the answer

64 is the answer