Mensuration
- A hemispherical bowl has 3.5 cm radius. It is to be painted inside as well as outside. The cost of painting it at the rate of Rs. 5 per 10 sq. cm will be:
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Inner and outer surface areas of the bowl = 4πr²
= 4 × 22 × 3.5 × 3.5 = 154 sq. cm. 7 ∴ Cost of painting = 154 × 5 = Rs. 77 10 Correct Option: A
Inner and outer surface areas of the bowl = 4πr²
= 4 × 22 × 3.5 × 3.5 = 154 sq. cm. 7 ∴ Cost of painting = 154 × 5 = Rs. 77 10
- The radius of base and curved surface area of a right cylinder is ‘r’ units and 4prh square units respectively. The height of the cylinder is :
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Curved surface area of cylinder = 2πRH
∴ According to the question, 2πrH = 4πrh
⇒ H = 2h unitsCorrect Option: C
Curved surface area of cylinder = 2πRH
∴ According to the question, 2πrH = 4πrh
⇒ H = 2h units
- A hemisphere and a cone have equal bases. If their heights are also equal, then the ratio of their curved surfaces will be
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Curved surface area of hemisphere = 2πr²
Curved surface area of cone = πrl = πr √r² + r²
[∵ h = r]
= √2πr²
∴ Required ratio = 2πr² : 2
√2πr = √32 : 1Correct Option: D
Curved surface area of hemisphere = 2πr²
Curved surface area of cone = πrl = πr √r² + r²
[∵ h = r]
= √2πr²
∴ Required ratio = 2πr² : 2
√2πr = √32 : 1
- There is a wooden sphere of radius 6√3cm. The surface area of the largest possible cube cut out from the sphere will be
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Diagonal of cube = Diameter of sphere = 6√3 × 2 = 12√3 cm.∴ Edge of cube = 12√3 = 12 cm. √3
∴ Surface area of cube = 6 × (edge)² = (6 × 12 × 12) sq. cm.
= 864 sq. cm.Correct Option: A
Diagonal of cube = Diameter of sphere = 6√3 × 2 = 12√3 cm.∴ Edge of cube = 12√3 = 12 cm. √3
∴ Surface area of cube = 6 × (edge)² = (6 × 12 × 12) sq. cm.
= 864 sq. cm.
- The base of a right pyramid is a square of side 10 cm. If the height of the pyramid is 12 cm, then its total surface area is
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Slant height = BE = √12 + 5 = √144 + 25
= √169 = 13 cm.∴ Lateral surface of pyramid = 1 × perimeter of base × slant height 2 = 1 × 40 × 13 = 260 sq. cm. 2
Area of base = 10 × 10 = 100 sq. cm.
∴ Total surface area = (260 + 100) sq. cm. = 360 sq. cm.Correct Option: D
Slant height = BE = √12 + 5 = √144 + 25
= √169 = 13 cm.∴ Lateral surface of pyramid = 1 × perimeter of base × slant height 2 = 1 × 40 × 13 = 260 sq. cm. 2
Area of base = 10 × 10 = 100 sq. cm.
∴ Total surface area = (260 + 100) sq. cm. = 360 sq. cm.
