Mensuration
- The total surface area of a regular triangular pyramid with each edge of length 1 cm is
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Total surface area = 4 × √3 × (1)³ = √3 sq.cm. 4 Correct Option: C
Total surface area = 4 × √3 × (1)³ = √3 sq.cm. 4
- The length, breadth and height of a wooden box with a lid are 10 cm, 9 cm and 7 cm, respectively. The total inner surface of the closed box is 262 cm2. The thickness of the wood (in cm.) is
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Let the thickness of wood = x cm.
∴ Area of the inner surface = 2 (9 – 2x) (10 – 2x) + 2 (9 –2x) (7 – 2x) + 2 (7 – 2x) (10– 2x)= 262
Putting x = 1, the equation is satisfied.Correct Option: D
Let the thickness of wood = x cm.
∴ Area of the inner surface = 2 (9 – 2x) (10 – 2x) + 2 (9 –2x) (7 – 2x) + 2 (7 – 2x) (10– 2x)= 262
Putting x = 1, the equation is satisfied.
- From a solid right circular cylinder of length 4 cm and diameter 6 cm, a conical cavity of the same height and base is hollowed out. The whole surface of the remaining solid (in square cm.) is
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Whole surface of the remaining solid = 2πrh + πr² + πrl
where l = slant height of cone. l = √r² + h² = √3² + 4²
= √9 + 16 = √25 = 5 cm
∴ Required area = (2 × π × 4 × 3 + π × 3 × 3 + π × 3 × 5) square cm.
= (24π + 9π + 15π) square cm. = 48π square cm.Correct Option: A
Whole surface of the remaining solid = 2πrh + πr² + πrl
where l = slant height of cone. l = √r² + h² = √3² + 4²
= √9 + 16 = √25 = 5 cm
∴ Required area = (2 × π × 4 × 3 + π × 3 × 3 + π × 3 × 5) square cm.
= (24π + 9π + 15π) square cm. = 48π square cm.
- There are two cones. The curved surface area of one is twice that of the other. The slant height of the latter is twice that of the former. The ratio of their radii is
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Curved surface area of first cone = πr1l1
Curved surface area of second cone = πr2l2
πr1l1 = 2πr2l2
π r1l1 = 2r2l2⇒ r1 = 2l2 = 2 × 2l1 = 4 = 4 : 1 r2 l1 l1 1 Correct Option: A
Curved surface area of first cone = πr1l1
Curved surface area of second cone = πr2l2
πr1l1 = 2πr2l2
π r1l1 = 2r2l2⇒ r1 = 2l2 = 2 × 2l1 = 4 = 4 : 1 r2 l1 l1 1
- The radius of a right circular cone is 3 cm and its height is 4 cm. The total surface area of the cone is
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OB = 3 cm
OA = 4 cm
∴ AB = l
= √3² + 4² = √9 + 16
= √25 = 5 cm
∴ Total surface area = πrl + πr² = πr(l +r)= 22 × 3(5 + 3) 7 = 22 × 3 × 8 = 75.4 sq.cm. 7 Correct Option: D
OB = 3 cm
OA = 4 cm
∴ AB = l
= √3² + 4² = √9 + 16
= √25 = 5 cm
∴ Total surface area = πrl + πr² = πr(l +r)= 22 × 3(5 + 3) 7 = 22 × 3 × 8 = 75.4 sq.cm. 7
