Volume and Surface Area of Solid Figures
- The diameter of the base of a right circular cylinder is 14 cm, while its length is 40 cm. Find the total surface area of the cylinder. ?
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Total surface area of cylinder = 2πr(h + r)
Given that, r = 14/2 = 7 cm, h = 40 cmCorrect Option: A
Total surface area of cylinder = 2πr(h + r)
Given that, r = 14/2 = 7 cm, h = 40 cm
∴ Required total surface area = 2 x (22/7) x 7 x (40 + 7)
= 44 x 47 = 2068 sq cm
- If the lateral surface area of a cylinder is 94.2 sq cm and its height is 5 cm, then find the radius of its base. (π = 3.14) ?
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Given, lateral surface area = 94.2 sq cm
⇒ 2πrh = 94.2
∴ r = 94.2/(2πh)Correct Option: C
Given, lateral surface area = 94.2 sq cm
⇒ 2πrh = 94.2
∴ r = 94.2/(2πh) = 94.2/(2 x 3.14 x 5) = 3 cm
- A rod of 2 cm diameter and 30 cm length is converted into a wire of 3 cm length of uniform thickness. The diameter of the wire is ?
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Given,
r1 = 1 cm, h1 = 30 cm, h2 = 300 cm.
Volume of rod = Volume of wire
⇒ πr12h1 = πr22h2
Correct Option: B
Given, r1 = 1 cm, h1 = 30 cm, h2 = 300 cm.
Volume of rod = Volume of wire
⇒ πr12h1 = πr22h2
⇒ π x (1)2 x 30 = π x r22 x 300
⇒ r22 = 30/300
∴ r2 = 1/√10 cm
∴ diameter = 2r2
= 2 x 1/√10 = 2/√10cm.
- What is the height of a solid cylinder of radius 5 cm and total surface area is 660 sq cm ?
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Let the height and radius and radius of solid cylinder be h and r cm respectively
Given that, radius (r) = 5 cm
and total surface area = 660 cm2
⇒ 2πrh + 2πr2 = 660Correct Option: D
Let the height and radius and radius of solid cylinder be h and r cm respectively
Given that, radius (r) = 5 cm
and total surface area = 660 cm2
⇒ 2πrh + 2πr2 = 660
⇒ 2πr(h + r) = 660
⇒ (h + 5) = 330/5π = 330/5 x 7/22
⇒ h = 66 x (7/22) - 5 = 21 - 5
∴ Required height = 16 cm
- What will be the curved surface area of a right circular cylinder having length 160 cm and radius of the base is 7 cm ?
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Curved surface area of the cylinder = 2πrh
Correct Option: D
Curved surface area of the cylinder = 2πrh
= 2 x (22/7) x 7 x 160
= 7040 sq cm