SSC CGL 201921)The internal diameter of a hollow hemispherical vessel is 24 cm. It is made of a steel sheet which is 0.5 cm thick, What is the total surface area (in \(cm^2\)) of the vessel?
\(612.75\pi\)
SSC CGL 201922)A sector of radius 10.5 cm with the central angle \(120^0\) is folded to form a cone by joining the two bounding radii of the sector. What is the volume (in \(cm^3\)) of the cone so formed?
\({343\sqrt2\over12}\pi\)
Radius of sector r = 10.5 cm
Circumference of sector whose angle is 120° = 2 πr × (θ/360) = 2 × (22/7) × 10.5 × (120/360) = 22cm
If we make cone from sector then,
Slant height (l) of the cone = radius of sector = 10.5 cm
Circumference of the cone = 22
2πr = 22, where r is the radius of cone
⇒ 2 × (22/7) × r = 22
⇒ r = 7/2 = 3.5 cm
As we know,
⇒ l2 = r2 + h2
⇒ (10.5)2 = (3.5)2 + h2
⇒ h2 = 110.25 – 12.25
⇒ h = 7 √2 cm
SSC CGL 201923)The area of the base of a right circular cone is \(400\pi\) and its height is 15 cm. The curved surface area of the cone (in \(cm^2\)) is:
\(500\pi\)
SSC CGL 201924)The base of a right prism is a triangle with sides 20 cm, 21 cm and 29 cm. If its volume is 7560 \(cm^3\), then its lateral surface area (in \(cm^2\)) is:
2520
SSC CGL 201925)A cylindrical vessel of radius 3.5 m is full of water. If 15400 litres of water is taken out from it, then the drop in the water level in the vessel will be:
40 cm
SSC CGL 201926)A solid metallic sphere of radius 8 cm is melted and drawn into a wire of uniform cross-section. If the length of the wire is 24 m, then its radius (in mm) is:
\(5\frac{1}{3}\)
SSC CGL 201927)The base of a right pyramid is an equilateral triangle with side 8 cm, and the height of the pyramid is \(24\sqrt3\) cm. The volume (in \(cm^3\)) of the pyramid is:
384
Volume of pyramid = (1/3) × Area of base × height
The base of a right pyramid is an equilateral triangle with side 8 cm, and the height of the pyramid is 24√3 cm.
Volume = (1/3) × (√3/4) × 82 × 24√3
⇒ 384 cm3
SSC CGL 201928)If the diameter of the base of a right circular cylinder is reduced by \(33\frac{1}{3}\)% and its height is doubled, then the volume of the cylinder will :
decrease by \(11\frac{1}{9}\)%
SSC CGL 201929)A right circular solid cone of radius 3.2 cm and height 7.2 cm is melted and recast into a right circular cylinder of height 9.6 cm. What is the diameter of the base of the cylinder?
3.2 cm.
SSC CGL 201930)A hemispherical bowl of internal diameter 36 cm is full of a liquid. This liquid is to be filled into cylindrical bottles each of radius 3 cm and height 12 cm. How many such bottles are required to empty the bowl?
36