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: #71

If the total surface area of a cube is 150 sq. cm., its volume will be ........ cubic cm.

Ans: 125

Question No: #72

The diagonal of each face of a cube is `2\sqrt{2}` cm, then the volume of the cube is -
(a) `4` cubic cm, (b) `16\sqrt{2}` cubic cm, (c) `16` cubic cm, (d) `8` cubic cm

Ans: (d) `8` cubic cm (ঘনসেমি)

Question No: #73

Find the total surface area of a cube whose diagonal is of length `4\sqrt{3}` cm .

Ans: 96 sq. cm.

Question No: #74

How many times the length of the diagonal of a cube is the length of the diagonal of a face of the cube?
(a) `\sqrt{3}`, (b) `\sqrt{2}`, (c) `\frac{\sqrt{6}}{2}`, (d) None of these

Ans: (c) `\frac{\sqrt{6}}{2}`

Question No: #75

If total surface area of a cube is `s` sq. unit and the length of its diagonal is `d` unit, then the relation between `s` and `d` is -
(a) `s = 6d^2`, (b) `3s = 7d`, (c) `s^3 = d^2`, (d) `d^2 = s/2`

Ans: (d) `d^2 = s/2`

Question No: #76

If the length of a diagonal of a cube is `D`, the total surface area is `S`, and the volume is `V`, what is the value of `{SD}/V`?

Ans: `6\sqrt{3}`

Question No: #77

Find the length of the largest rod that can fit in a room measuring 30 m × 24 m × 18 m.

Ans: `30\sqrt{2}` m.

Question No: #78

The length of longest rod can be placed inside a cube is `4\sqrt{3}` cm. Find the volume of the cube.

Ans: 64 cc

Question No: #79

The volume of a rectangular parallelopiped is `v` cubic unit. The length, breadth and height of it is `a`, `b` and `c` unit respectively and its surface area is `s` sq. unit, then prove that, `1/v = 2/s (1/a + 1/b + 1/c)` ।

Ans:

Question No: #80

Two cubes whose length of the edges are equal are combined side by side to form a rectangular parallelopiped. If the volume of the rectangular parallelopiped is 1024 c.c. then find the edge of each cube.

Ans: 8 cm.