Surface areas and volumes of solids - class-X

Question 1 Multiple Choice (Single Answer)

From a solid sphere of radius $R$, a concentric solid sphere of radius $\dfrac{R}{2}$ is removed. The total surface area increases by

$0%$
$25%$
$50%$
$75%$

Question 2 Multiple Choice (Single Answer)

The volume of triangular prism whose adjacent sides are $\bar a,\ \bar b,\ \bar c$ each of magnitude $4$ units and each is inclined at an angel $\dfrac {\pi}{3}$ with other two is

$16\sqrt {2}$
$16\sqrt {3}$
$8\sqrt {3}$
$8\sqrt {2}$

Question 3 Multiple Choice (Single Answer)

If a regular square pyramid has a base of side $8 cm$ and height of $30 cm$, then its volume is

$120 cm^3.$
$240 cm^3.$
$640 cm^3.$
$900 cm^3.$

Question 4 Multiple Choice (Single Answer)

A square pyramid can contain $16\ m^3$ of water. The height of the pyramid is $3\ m$. Calculate the length of base of the square pyramid.

$16\ m$
$12\ m$
$4\ m$
$2\ m$

Question 5 Multiple Choice (Single Answer)

$VPQRS$ is rectangle based pyramid where $PQ = 30\ cm, QR = 20\ cm$ and volume is $2000\ {cm}^3$, then height (in cm) is

$20$
$40$
$10$
$30$

Question 6 Multiple Choice (Single Answer)

State whether true or false :

If $s$ is the perimeter of the base of a prism, $n$ is the number of sides of the base, $S$ is the total length of the edges and $h$ is the height, then $S=nh+2s$.

True
False

Question 7 Multiple Choice (Single Answer)

The base of right prism is a triangle whose perimeter is 28 cm and the inradius of the triangle is 4 cm. If the volume of the prism is 366 cc, then its height is

6.54 cm
8 cm
4 cm
None of these

Question 8 Multiple Choice (Single Answer)

The slant height of a right pyramid having square base of side $10cm$ and vertical height $15cm$ is

$5\sqrt{10}cm$
$6\sqrt{10}cm$
$7\sqrt{10}cm$
$8\sqrt{10}cm$

Question 9 Multiple Choice (Single Answer)

Consider an incomplete pyramid of balls on a square base having $18$ players, and having $13$ balls on each side of the top layer. Then the total number $N$ of balls in that pyramid satisfies

$ 9000 < N <10000$
$8000 < N < 9000$
$7000 < N < 8000$
$ 10000 < N < 12000 $

Question 10 Multiple Choice (Single Answer)

The circumference of a 1 cm thick pipe is 44 cm. The level of water that 7 cm of pipe can hold is

$798 cm^3$
$308 cm^3$
$792 cm^3$
$795 cm^3$

Question 11 Multiple Choice (Single Answer)

The base of a right prism is a square of perimeter 20 cm and its height is 30 cm. The volume of the prism is

$700 cm^3$
$750 cm^3$
$800 cm^3$
$850 cm^3$

Question 12 Multiple Choice (Single Answer)

The base of a right prism is an equilateral triangle of edge $12$m. If the volume of the prism is $288\sqrt 3m^3$, then its height is:

$6$m
$8$m
$10$m
$12$m

Surface areas and volumes of solids - class-X

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