Question

A Room is 30m long, 24 m broad and 18 m high. Find:
(a) length of the longest rod that can be placed in the room.
(b) its total surface area.
(c) its volume.​

Answer 1

GIVEN :-

• Length (l) = 30m
• Breadth (b) = 24m
• Height (h) = 18m

SOLUTION :-

(a) Length of the longest rod that can be placed in the room.

$\\ \bigstar \boxed{\sf \:length \: of \: longest \: rod = \sqrt{ {l}^{2} + {b}^{2} + {h}^{2} } }$

$\\ \implies\sf \: \sqrt{ {30}^{2} + {24}^{2} + {18}^{2} } \\ \\ \implies \sf \: \sqrt{900 + 576 + 324} \\ \\ \implies \sf \: \sqrt{1800}$

$\implies \sf \: \sqrt{10 \times 10 \times 3 \times 3 \times 2} \\ \\ \implies \sf \: 10 \times 3 \sqrt{2} \\ \\ \implies\sf \: 30 \sqrt{2} m$

Hence , length of the longest rod that can be fit in the room is 30√2m.

(b) Total Surface Area (TSA) of room.

Room is in the form of Cuboid.

$\\ \bigstar \boxed{ \sf \: Total \: Surface \: Area \: of \: Cuboid = 2(lh + bh + lb)}$

$\\ \implies \sf \: 2 \{(30)(18) + (24)(18) + (30)(24) \} \\ \\ \implies \sf \: 2(540 + 432 + 720) \\ \\ \implies \sf \: 2(1692) \\ \\ \implies \sf \: 3384 {m}^{2}$

Hence , T.S.A of room is 3384m².

(c) Volume of room.

$\\ \bigstar \boxed{ \sf \: volume \:of \: cuboid = l \times b \times h }$

$\\ \implies \sf \: 30 \times 24 \times 18 \\ \\ \implies\sf \:12960 {m}^{3}$

Hence , volume of room is 12960m³.

Answer 2

Given :

• Length of Cuboid (l) = 30m
• Breadth of Cuboid (b) = 24m
• Height of Cuboid (h) = 18m

To Find :

• Length of the longest rod that can be placed in the room.
• Its total surface area.
• Its volume.

Solution :

a) Length of the longest rod that can be placed in the room

✰ Length of the longest rod that can be placed in the room is nothing but the diagonal of the room. So we will find the Diagonal of the room.

⟹ Diagonal = √(l)² + (b)² + (h)²

⟹ Diagonal = √(30)² + (24)² + (18)²

⟹ Diagonal = √900 + 576 + 324

⟹ Diagonal = √900 + 900

⟹ Diagonal = √900 + 900

⟹ Diagonal = √1800

⟹ Diagonal = 42.42m {approx}

Thus Length of the longest rod that can be placed in the room is 42.42m

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b) It's Total Surface Area

✰ As we know that, Total Surface Area (TSA) of Cuboid is given by 2(lb + bh + lh) . So Simply we will fill the values in the formula to find the Total Surface Area of Cuboid.

➟ TSA = 2(lb + bh + lh)

➟ TSA = 2(30 × 24 + 24 × 18 + 30 × 18)

➟ TSA = 2(720 + 432 + 540)

➟ TSA = 2(720 + 972)

➟ TSA = 2× 1692

➟ TSA = 3384m²

Thus Total Surface Area of Cuboid is 3384m²

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c) It's Volume

✰ As we know that, Volume of Cuboid is given by Length × Breadth × Height . So Simply we will put the values in the formula to find the Volume of Cuboid.

➣ Volume = L × B × H

➣ Volume = 30 × 24 × 18

➣ Volume = 30 × 432

➣ Volume = 12960m³

Thus Volume of Cuboid is 12960m³

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