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Find the total surface area, volume and length of diagonal of a cuboid whose length, breadth and height are 16 cm. 12 cm. and 4 cm. respectively.
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A) \( \Large 688\ cm^{2} \), \( \Large 784\ cm^{3} \), 24.8 cm. |
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B) \( \Large 608\ cm^{2} \), \( \Large 768\ cm^{3} \), 20.4 cm. |
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C) \( \Large 664\ cm^{2} \), \( \Large 754\ cm^{3} \), 32.6 cm. |
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D) \( \Large 672\ cm^{2} \), \( \Large 772\ cm^{3} \), 48.6 cm. |
Correct Answer:
| B) \( \Large 608\ cm^{2} \), \( \Large 768\ cm^{3} \), 20.4 cm. |
Description for Correct answer:
l = 16 cm, b = 12 cm, h = 4 cm
Total surface area = \( \Large 2 \left(lb+bh+hl\right) \)
= \( \Large 2 \left(192+48+64\right) \)
=\( \Large 2 \times 304 = 608\ cm^{2} \)
Volume of the cuboid = \( \Large lbh = 16 \times 12 \times 4 \)
= \( \Large 16 \times 48 = 768\ cm^{3} \)
Length of the diagonal = \( \Large \sqrt{l^{2}+b^{2}+h^{2}} \)
=\( \Large \sqrt{16^{2}+12^{2}+4^{2}} \)
=\( \Large \sqrt{256+144+16} \)
=\( \Large \sqrt{416} \) = 20.4 cm.
l = 16 cm, b = 12 cm, h = 4 cm
Total surface area = \( \Large 2 \left(lb+bh+hl\right) \)
= \( \Large 2 \left(192+48+64\right) \)
=\( \Large 2 \times 304 = 608\ cm^{2} \)
Volume of the cuboid = \( \Large lbh = 16 \times 12 \times 4 \)
= \( \Large 16 \times 48 = 768\ cm^{3} \)
Length of the diagonal = \( \Large \sqrt{l^{2}+b^{2}+h^{2}} \)
=\( \Large \sqrt{16^{2}+12^{2}+4^{2}} \)
=\( \Large \sqrt{256+144+16} \)
=\( \Large \sqrt{416} \) = 20.4 cm.
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