Miscellaneous Mensuration (Simple) | Learn Mathematics Online

Miscellaneous Mensuration (Simple)

Study Material (PDF)

Study Material (PDF)

Click on each question to see answer & solution.

Question No: #141

If the height and base radius are the same, then the ratio of volume of a cone and a cylinder is -
(a) `1:2`, (b) `2:1`, (c) `3:1`, (d) `1:3`

Ans: (d) `1:3`

Question No: #142

If the ratio of radius of the base of a right circular cylinder and a right circular cone is `3:4` and the ratio of their height is `2:3`, then find the ratio of their volume.

Ans: `9:8`

Question No: #143

The volume of a sphere `4/3 \pi r^3` cubic unit. If it is placed inside a cube, then the ratio of volume of cube and sphere is -
(a) `3:\pi`, (b) `4:\pi`, (c) `6:\pi`, (d) `8:\pi`

Ans: `6:\pi`

Question No: #144

The volume of the largest solid cone that can be cut off from a solid hemisphere of radius `r` will be -
(a) `4/3 \pi r^3` cubic unit, (b) `3 \pi r^3` cubic unit, (c) `{\pi r^3}/4` cubic unit, (d) `{\pi r^3}/3` cubic unit

Ans: (d) `{\pi r^3}/3` cubic unit

Question No: #145

If the largest sphere is cut out of a certain hemisphere of radius `r`, then the ratio of the volume of the sphere to the hemisphere will be -
(a) `1:6`, (b) `1:4`, (c) `1:9`, (d) `2:3`

Ans: (b) `1:4`

Question No: #146

Find the volume of the largest cube that can be cut from a metal sphere of radius `4\sqrt{2}` cm.

Ans: `\frac{1024\sqrt{2}}{3\sqrt{3}}` c.c.

Question No: #147

Find the volume of the largest right circular cone that can be cut out from a cube of wood of edge 42 cm.

Ans: 19404 c.c.

Question No: #148

A cylindrical wooden log of `12\sqrt{2}` cm. diameter and 21 m. long is taken to make it a rectangular parallelopiped shape having a square cross section. If minimum wood is lost, then find how much wood will be there (rectangular parallelopiped shape) and what is the loss?

Ans: 302.4 cubic dcm, 172.8 cubic dcm

Question No: #149

The cross-section of a rectangular parallelopiped wooden log of 2m. length is a square and each of its side is 14 dcm. in length. If this log can be converted into a right circular log by wasting minimum amount of wood, then let us calculate what amount of wood (in cubic-meter) will be remained in it and what amount of wood (in cubic-meter) will be wasted.

Ans: 3.08 cubic-meter, 0.84 cubic-meter

Question No: #150

A solid is hemispherical at the bottom and conical (of same radius) above it .If the surface areas of the two parts are equal, then find the ratio of its radius and the height of the conical part.

Ans: `1:\sqrt{3}`