2. The volume of a right prism is 1320 cu. inches and its base trapezium whose parallel sides are of lengths 8 inches and I 4 inches. If the third side of the trapezium be perpendicular to the parallel sides and is of length 8 inches, find the height of the prism and the area of its lateral surface.
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Solution: Let the base of the right prism be the trapezium ABCD whose parallel sides are AB and DC and the third side DA is perpendicular to both AB and DC.
volume of prism
Draw CE perpendicular to AB. By question.
DC = 8, AB = 14 and DA = 8
Therefore, AE = DC = 8, CE = DA = 8
And EB = AB - AE = 14 – 8 = 6
Now , from the right - angled CEB we get,
BC² = CE² + EB² = 8² + 6² = 100
Or, BC = 10
Again, the area of trapezium ABCD
= 1/2 × (sum of the lengths of the parallel sides) × (distance between the parallel sides)
= 1/2 × (AB + DC) × AD
= 1/2 (14 + 8) × 8
= 88 sq. inches.
Let h be the required height of the right prism. Then, volume of the prism = area of its base × its height.
or, 1320 = 88 × h [Since, volume of the prism = 1320 cu. Inches (given)]
Therefore, h = 1320/88 = 15.
Therefore the required height of the prism is 15 inches.
Again , the area of the lateral surface of the prism
= (perimeter of its base) × its height
= (AB + BC + CD + DA ) × 15
= (14 + 10 + 8 + 8) × 15
= 40 × 15
= 600 sq. inches.
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“ɴᴇᴠᴇʀ ꜱᴛᴏᴘꜱ ʟᴇᴀʀɴɪɴɢ, ʙᴇᴄᴀᴜꜱᴇ ʟɪꜰᴇ ɴᴇᴠᴇʀ ꜱᴛᴏᴘꜱ ᴛᴇᴀᴄʜɪɴɢ”
Solution: Let the base of the right prism be the trapezium ABCD whose parallel sides are AB and DC and the third side DA is perpendicular to both AB and DC.
volume of prism
Draw CE perpendicular to AB. By question.
DC = 8, AB = 14 and DA = 8
Therefore, AE = DC = 8, CE = DA = 8
And EB = AB - AE = 14 – 8 = 6
Now , from the right - angled CEB we get,
BC² = CE² + EB² = 8² + 6² = 100
Or, BC = 10
Again, the area of trapezium ABCD
= 1/2 × (sum of the lengths of the parallel sides) × (distance between the parallel sides)
= 1/2 × (AB + DC) × AD
= 1/2 (14 + 8) × 8
= 88 sq. inches.
Let h be the required height of the right prism. Then, volume of the prism = area of its base × its height.
or, 1320 = 88 × h [Since, volume of the prism = 1320 cu. Inches (given)]
Therefore, h = 1320/88 = 15.
Therefore the required height of the prism is 15 inches.
Again , the area of the lateral surface of the prism
= (perimeter of its base) × its height
= (AB + BC + CD + DA ) × 15
= (14 + 10 + 8 + 8) × 15
= 40 × 15
= 600 sq. inches.
⚘ ᴄʜᴇꜱᴋᴀ ⚘
“ɴᴇᴠᴇʀ ꜱᴛᴏᴘꜱ ʟᴇᴀʀɴɪɴɢ, ʙᴇᴄᴀᴜꜱᴇ ʟɪꜰᴇ ɴᴇᴠᴇʀ ꜱᴛᴏᴘꜱ ᴛᴇᴀᴄʜɪɴɢ”