the length breadth and height of a cuboid are in the ratio of 7:5:2 its volume is 35840cmsq.find its dimensions About the author Caroline
ǫᴜᴇsᴛɪᴏɴ-: The length breadth and height of a cuboid are in the ratio of 7:5:2 its volume is 35840cmsq.find its dimensions sᴏʟᴜᴛɪᴏɴ-: ★Let the length,breadth and height of the cuboid be 5x , 3x and 2x respectively. ★We know that the volume of the cuboid is [tex]\sf{l \times b\times h}[/tex] ★It is given that the volume of the cuboid is [tex]\sf{35.937m^2}[/tex] , therefore. [tex]\sf{35.937~=~5x \times 3x\times 2x}[/tex] ⇝[tex]30x^3[/tex] = [tex]35.937[/tex] ⇝[tex]x^3[/tex] = [tex]\frac{35.937}{30}[/tex] = [tex]1.197[/tex] ⇝x = [tex]\sqrt{3}{1.197}[/tex] ⇝x = [tex]0.33[/tex] ★Therefore, the length l = 5x = 5 × 0.33 = 1.65, ★breadth b = 3x = 3 × 0.33 = 0.99 and ★height h = 2x = 2 × 0.33 = 0.66 ★Now, the total surface area of cuboid is 2(lb + bh + hl), therefore, the total surface area with length 1.65 m, breadth 0.99 m and height 0.66 m is: ★A = 2[(1.65×0.99) + (0.99×0.66) + (0.99×1.65)] = 2(1.6335+0.6534+1.089) = 2×3.3759 = [tex]\sf6.7518m^2[/tex] ★Hence, the dimensions of cuboid is 1.65 m, 0.99 m and 0.66 m and the total surface area of cuboid is 6.7518 m Reply
Answer: Step-by-step explanation: Answer : The volume of cuboid is 5670 cm³ Step-by-step explanation : Let the length, breath and height of the cuboid be 7x, 6x and 5x respectively. According to the question ; Surface area of cuboid = 1926 cm² ⇒ 2 ( lb + bh + hl ) = 1926 ⇒ 2 ( 7x * 6x + 6x * 5x + 5x * 7x ) = 1926 ⇒ ( 42 x² + 30 x² + 35x² ) = 1926 / 2 ⇒ 107 x² = 963 ⇒ x² = 963 / 107 ⇒ x² = 9 ⇒ x = √9 ⇒ x = 3 Therefore, the length, breath and height of the cuboid are ; Length (l) = 7 * 3 = 21 cm. Breadth (b) = 6 * 3 = 18 cm. Height (h) = 5 * 3 = 15 cm. Volume of cuboid = l × b × h = 21 × 18 × 15 = 5670 cm³ Reply
ǫᴜᴇsᴛɪᴏɴ-:
The length breadth and height of a cuboid are in the ratio of 7:5:2 its volume is 35840cmsq.find its dimensions
sᴏʟᴜᴛɪᴏɴ-:
★Let the length,breadth and height of the cuboid be 5x , 3x and 2x respectively.
★We know that the volume of the cuboid is [tex]\sf{l \times b\times h}[/tex]
★It is given that the volume of the cuboid is [tex]\sf{35.937m^2}[/tex] , therefore.
[tex]\sf{35.937~=~5x \times 3x\times 2x}[/tex]
⇝[tex]30x^3[/tex] = [tex]35.937[/tex]
⇝[tex]x^3[/tex] = [tex]\frac{35.937}{30}[/tex] = [tex]1.197[/tex]
⇝x = [tex]\sqrt{3}{1.197}[/tex]
⇝x = [tex]0.33[/tex]
★Therefore, the length l = 5x = 5 × 0.33 = 1.65,
★breadth b = 3x = 3 × 0.33 = 0.99 and
★height h = 2x = 2 × 0.33 = 0.66
★Now, the total surface area of cuboid is 2(lb + bh + hl),
therefore, the total surface area with length 1.65 m, breadth 0.99 m and height 0.66 m is:
★A = 2[(1.65×0.99) + (0.99×0.66) + (0.99×1.65)] = 2(1.6335+0.6534+1.089) = 2×3.3759 = [tex]\sf6.7518m^2[/tex]
★Hence, the dimensions of cuboid is 1.65 m, 0.99 m and 0.66 m and the total surface area of cuboid is 6.7518 m
Answer:
Step-by-step explanation:
Answer :
The volume of cuboid is 5670 cm³
Step-by-step explanation :
Let the length, breath and height of the cuboid be 7x, 6x and 5x respectively.
According to the question ;
Surface area of cuboid = 1926 cm²
⇒ 2 ( lb + bh + hl ) = 1926
⇒ 2 ( 7x * 6x + 6x * 5x + 5x * 7x ) = 1926
⇒ ( 42 x² + 30 x² + 35x² ) = 1926 / 2
⇒ 107 x² = 963
⇒ x² = 963 / 107
⇒ x² = 9
⇒ x = √9
⇒ x = 3
Therefore, the length, breath and height of the cuboid are ;
Length (l) = 7 * 3 = 21 cm.
Breadth (b) = 6 * 3 = 18 cm.
Height (h) = 5 * 3 = 15 cm.
Volume of cuboid = l × b × h
= 21 × 18 × 15
= 5670 cm³