Online Test — Mensuration
10 Questions • 15 min • Chapter MCQ
15:00
Question 1 of 10
medium
A solid capsule is made by attaching two hemispheres to the ends of a cylinder. Its total volume is equal to...
Vol(Cyl) + Vol(Hemi)
Vol(Cyl) + 2 $\cdot$ Vol(Hemi)
CSA(Cyl) + TSA(Hemi)
2 $\cdot$ Vol(Cyl) + Vol(Hemi)
Explanation: The space inside is the sum of the cylindrical core plus both hemispherical end caps.
Question 2 of 10
medium
If a solid right cone is chopped by a flat plane parallel to its circular base, the lower remaining chunk is a...
Cylinder
Sphere
Frustum
Cuboid
Explanation: By definition, the lower sliced base portion of a cone is a frustum.
Question 3 of 10
medium
When a solid metal cube is melted down and recast into a cylinder, which property stays perfectly constant?
Surface Area
Slant Height
Volume
Base Perimeter
Explanation: Recasting matter preserves the total three-dimensional volume capacity.
Question 4 of 10
medium
Find the volume of a frustum of a cone with height 3 cm and base radii 4 cm and 2 cm. (Leave in terms of $\pi$).
$7\pi$ cubic cm
$14\pi$ cubic cm
$28\pi$ cubic cm
$56\pi$ cubic cm
Explanation: Vol = $(1/3)\pi(3)(4^2 + 2^2 + 4\cdot2) = \pi(16 + 4 + 8) = 28\pi$ cubic cm.
Question 5 of 10
medium
A solid sphere of radius 3 cm is melted to form a cone of base radius 3 cm. Find the height of the cone.
3 cm
6 cm
9 cm
12 cm
Explanation: $(4/3)\pi(3^3) = (1/3)\pi(3^2)h \implies 4 \cdot 27 = 9h \implies 108 = 9h \implies h = 12$ cm.
Question 6 of 10
medium
Find the slant height of a frustum of a cone if its vertical height is 4 cm, $R = 7$ cm, and $r = 4$ cm.
5 cm
7 cm
6 cm
sqrt(41) cm
Explanation: Slant height $l = \sqrt{4^2 + (7 - 4)^2} = \sqrt{16 + 9} = \sqrt{25} = 5$ cm.
Question 7 of 10
medium
How many cubes of side 2 cm can be made by melting a large metal cuboid block of size 8 cm $\cdot$ 4 cm $\cdot$ 2 cm?
4
8
12
16
Explanation: Number $n = \frac{\text{Volume of cuboid}}{\text{Volume of cube}} = \frac{8 \cdot 4 \cdot 2}{2 \cdot 2 \cdot 2} = \frac{64}{8} = 8$.
Question 8 of 10
medium
A toy is formed by joining a cone and a hemisphere along their identical bases. The visible outer surface area is...
TSA(Cone) + TSA(Hemi)
CSA(Cone) + CSA(Hemi)
CSA(Cone) + TSA(Hemi)
TSA(Cone) + CSA(Hemi)
Explanation: The flat circular bases are hidden inside the joint, leaving only the two CSAs visible.
Question 9 of 10
medium
If the radii of the two circular ends of a frustum bucket are $R$ and $r$, what is the total area of its two flat bases?
$\pi(R + r)$
$\pi(R^2 - r^2)$
$\pi R^2 + \pi r^2$
$2\pi(R + r)$
Explanation: The two bases are distinct circles, so their combined area is $\pi R^2 + \pi r^2$.
Question 10 of 10
medium
If a solid cylinder of radius $r$ and height $h$ is melted down into a sphere of radius $r$, what is the value of $h$?
$(2/3)r$
$(4/3)r$
$2r$
$4r$
Explanation: $\pi r^2h = (4/3)\pi r^3 \implies h = (4/3)r$.