Scholastic Aptitude Test - Mathematics - Volume and Surface Area

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