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: #31

If the ratio of the volumes of two right-circular cones is `1:4` and the ratio of the lengths of their base radii is `4:5`, the ratio of their heights will be -
(a) `1:5`, (b) `5:4`, (c) `25:16`, (d) `25:64`

Ans: (d) `25:64`

Question No: #32

If the length of radius of a right circular cone be `r/2` unit and its slant height be `2l` unit, then total surface area will be -
(a) `2 \pi r (l+r)` sq. unit, (b) `\pi r (l + r/4)` sq. unit, (c) `\pi r (l+ r)` sq. unit, (d) `2 \pi r l` sq. unit

Ans: (b) `\pi r (l + r/4)` sq. unit

Question No: #33

The base area, height and volume of a right circular cone is `A`, `H` and `V` respectively. Find the value of `\frac{V}{AH}` -
(a) `1`, (b) `1/2`, (c) `1/3`, (d) `3`

Ans: (c) `1/3`

Question No: #34

The numerical values of the volume and the lateral surface area of a right circular cone are equal. If the height and the radius of the cone are `h` unit and `r` unit respectively, then find the value of `(1/h^2 + 1/r^2)`.

Ans: `1/9`

Question No: #35

If the height, slant height and diameter of base of a right circular cone are `h, l, d` respectively, then find the value of `\frac{l^2 - h^2}{d^2}`.

Ans: `1/4`

Question No: #36

If the base area, lateral surface area and slant height of a right-circular cone is `A`, `P` and `l` respectively, then show that `P^2 = \pi A l^2`.

Ans:

Question No: #37

If the height and radius of base of a right circular cone are equal, then what is the value of its vertical angle?

Ans: `90^\circ`

Question No: #38

If the radius and semi-vertical angle of a right circular cone is `2\sqrt{2}` cm and `45°` respectively, then find the slant height of this cone.

Ans: 4 cm

Question No: #39

If the vertical angle and radius of the base of a right circular cone are 60° and 14 cm respectively, then the curved surface area of this cone is ............

Ans: 1232 sq. cm.

Question No: #40

Doubling the height of a right-circular cone while keeping the length of the radius the same will increase the volume of the cone by -
(a) `100%`, (b) `200%`, (c) `300%`, (d) `400%`

Ans: `100%`