Mensuration
- There is a pyramid on a base which is a regular hexagon of side 2a cm. If every slant edge of this pyramid is of length 5a/2 cm, then the volume of this pyramid is
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Area of the base = 6 × √3 × (2a)² 4 = 6 × √3 × 4² = 6√3² sq.cm. 4 Height = √ 
5a 
² - (2a)² 2 = √ 25 a² - 4a² 4 = √ 9a² 4 = 3 a cm. 2 ∴ Volume of pyramid = 1 × area of base × height 3 ∴ Volume of pyramid = 1 × 6√3a² × 3 a 3 2
= 3√3a³cm³Correct Option: C
Area of the base = 6 × √3 × (2a)² 4 = 6 × √3 × 4² = 6√3² sq.cm. 4 Height = √ 5a ² - (2a)² 2 = √ 25 a² - 4a² 4 = √ 9a² 4 = 3 a cm. 2 ∴ Volume of pyramid = 1 × area of base × height 3 ∴ Volume of pyramid = 1 × 6√3a² × 3 a 3 2
= 3√3a³cm³
- The base of a right pyramid is a square of side 40 cm long. If the volume of the pyramid is 8000 cm³, then its height is :
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Area of the base = 40 × 40 = 1600 sq.cm
We know,∴ Volume of pyramid = 1 × area of base × height 3 ⇒ 8000 = 1 × 1600 × h 3 ⇒ h = 8000 × 3 = 15 cm. 1600 Correct Option: C
Area of the base = 40 × 40 = 1600 sq.cm
We know,∴ Volume of pyramid = 1 × area of base × height 3 ⇒ 8000 = 1 × 1600 × h 3 ⇒ h = 8000 × 3 = 15 cm. 1600
- The base of a right prism is a trapezium. The length of the parallel sides are 8 cm and 14 cm and the distance between the parallel sides is 8 cm. If the volume of the prism is 1056 cm³, then the height of the prism is
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Area of the base = 1 (sum of parallel sides) ×( per-pendicular distance) 2 = 1 (14 + 8) × 8 = 88 sq.cm. 2
∴ Volume = Area of the base × height
⇒ 1056 = 88 × h→ h = 1056 = 12 cm 88 Correct Option: C
Area of the base = 1 (sum of parallel sides) ×( per-pendicular distance) 2 = 1 (14 + 8) × 8 = 88 sq.cm. 2
∴ Volume = Area of the base × height
⇒ 1056 = 88 × h→ h = 1056 = 12 cm 88
- The height of a right prism with a square base is 15 cm. If the area of the total surface of the prism is 608 sq. cm, its volume is
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Total surface area of prism = Curved surface area + 2 × Area of base
⇒ 608 = perimeter of base × height + 2 × Area of base
⇒ 608 = 4x × 15 + 2x² (Where x = side of square)
⇒ x² + 30x – 304 = 0
⇒ x² + 38x – 8x – 304 = 0
⇒ x (x + 38) – 8 (x + 38) = 0
⇒ (x – 8) (x + 38) = 0
⇒ x = 8
⇒ Volume of prism = Area of base × height = 8 × 8 × 15 = 960 cu.cm.Correct Option: C
Total surface area of prism = Curved surface area + 2 × Area of base
⇒ 608 = perimeter of base × height + 2 × Area of base
⇒ 608 = 4x × 15 + 2x² (Where x = side of square)
⇒ x² + 30x – 304 = 0
⇒ x² + 38x – 8x – 304 = 0
⇒ x (x + 38) – 8 (x + 38) = 0
⇒ (x – 8) (x + 38) = 0
⇒ x = 8
⇒ Volume of prism = Area of base × height = 8 × 8 × 15 = 960 cu.cm.
- The base of right prism is a triangle whose perimeter is 28 cm and the inradius of the triangle is 4 cm. If the volume of the prism is 366 cc, then its height is
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Volume of prism = Area of base × height
⇒ 366 = 1 × 4 × 28 × h 2 ⇒ h = 366 = 6.53 cm 56 Correct Option: D
Volume of prism = Area of base × height
⇒ 366 = 1 × 4 × 28 × h 2 ⇒ h = 366 = 6.53 cm 56
