Scholastic Aptitude Test - Mathematics - Volume and Surface Area

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Question - 1

A hemispherical bowl is filled to the brim with a beverage. The contents of the bowl are transferred into a cylindrical vessel whose radius is 50% more than its height. If the diameter is same for both the bowl and the cylinder, the volume of the beverage in the cylindrical vessel is

  • A 66\(\frac{2}{3}\)%
  • B 78\(\frac{1}{2}\)%
  • C 100%
  • D none of these

Question - 2

A hemisphere and a cone have equal bases. If their heights are also equal, then the ratio of their curved surfaces will be

  • A 1:2
  • B 2:1
  • C 1:\(\sqrt2\)
  • D \(\sqrt2\):1

Question - 3

A cone of height 9 cm with diameter of its base is carved out from a wooden solid sphere of radius 9 cm. The percentage of wood wasted is

  • A 25%
  • B 25.5%
  • C 50%
  • D 75%

Question - 4

The number of coins of radius 0.75 cm and thickness 0.2 cm to be melted to make a right circular cylinder of height 8 em and base radius 3 cm is

  • A 460
  • B 500
  • C 600
  • D 640

Question - 5

The slant height of a conical mountain is 2.5 km and the area of its base is 1.54 krn2, The height of the mountain is

  • A 2.2 km
  • B 2.4 km
  • C 3 km
  • D 3.11 km

Question - 6

A solid metallic spherical ball of diameter 6 cm is melted and recast into a cone with diameter of the base as.12 cm. The height of the cone is

  • A 2 cm
  • B 3 cm
  • C 4 cm
  • D 6 cm

Question - 7

The diameter of the iron ball used for the shot-put game is 14 cm. It is melted and then a solid cylinder of height 2 1/3 cm is made. What will be the diameter of the base of the cylinder?

  • A 14 cm
  • B 14/3 cm
  • C 28 cm
  • D 28/3 cm

Question - 8

A metallic hemisphere is melted and recast in the shape of a cone with the same base radius (R) as that of the hemisphere. If H is the height of the cone, then

  • A H=2R
  • B H=3R
  • C H=\(\sqrt{3}\) R
  • D H=\(\frac{2}{3}\)R

Question - 9

A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. The height of the cone is

  • A 12 cm
  • B 14 cm
  • C 15 cm
  • D 18 cm

Question - 10

In what ratio are the volu.mes of a cylinder, a cone and a sphere, if each has the same diameter and the same height?

  • A 1:3:2
  • B 2:3:1
  • C 3:1:2
  • D 3:2:1
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