Volume of prism and pyramid - class-X

Practice calculating volumes of prisms and pyramids, including various base shapes, frustums, and understanding the relationship between prism and pyramid volumes.

21 Questions Published

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Questions

Question 1 Multiple Choice (Single Answer)

A frustum of a pyramid has an upper base $100\ m$ by $10\ m$ and a lower base of $80\ m$ by $8\ m$. if the altitude of the frustum is $5\ m$, find its volume (in cu. m).

$4567.67$
$3873.33$
$4066.67$
$2345.98$

Question 2 Multiple Choice (Single Answer)

A regular triangular pyramid has an altitude of $9\ m$ and a volume of $187.06\ cu.\ m$. What is the base edge in meters?

$12$
$13$
$14$
$15$

Question 3 Multiple Choice (Single Answer)

The frustum of a regular triangular pyramid has equilateral triangles for its bases. The lower and upper base edges are $9\ m$ and $3\ m$, respectively. If the volume is $118.2\ cu.\ m$, how far apart (m) are the base?

$9$
$8$
$7$
$10$

Question 4 Multiple Choice (Single Answer)

A regular hexagonal pyramid whose base perimeter is $60\ cm$ has an altitude of $30\ cm$, the volume of the pyramid (in cu. cm)is:

$2958$
$2598$
$2859$
$2589$

Question 5 Multiple Choice (Single Answer)

A pyramid whose base is a regular pentagon of area $42\ {cm}^2$ and whose height is $7$ cm. What is the volume (in ${cm}^3$) of the pyramid?

$98$
$105$
$126$
$147$

Question 6 Multiple Choice (Single Answer)

General formula of volume of a prism is:

Area of base $\times$ height
Area of triangle $\times$ height
Area of square $\times$ height
Area of rectangle $\times$ height

Question 7 Multiple Choice (Single Answer)

If base and height of a prism and pyramid are same, then the volume of a pyramid is:

$\dfrac{1}{3}\times$ Volume of prism
${3}\ \times$ Volume of prism
$\dfrac{1}{2}\times$ Volume of prism
$2\ \times$ Volume of prism

Question 8 Multiple Choice (Single Answer)

General formula to find volume of a pyramid is:

$\dfrac{\text{Base Area} \times \text{Height}}{2}$
$2(\text{Base Area} \times \text{Height})$
$\dfrac{\text{Base Area} \times \text{Height}}{3}$
$3(\text{Base Area} \times \text{Height})$

Question 9 Multiple Choice (Single Answer)

The base of the right pyramid is a square of side 16 cm and height 15 cm. Its volume $(cm^{3})$ will be

$3840$
$1920$
$1280$
$960$

Question 10 Multiple Choice (Single Answer)

The base of a right pyramid is an equilateral triangle of perimeter $8$ dm and the height of the pyramid is $30$$\sqrt{3}$ cm. The volume of the pyramid is

$1600$ cm$^{3}$
$16000$ cm$^3$
$\displaystyle \frac{16000}{3} cm^3$
$\displaystyle \frac{5}{4} cm^3$

Question 11 Multiple Choice (Single Answer)

A right pyramid is on a regular hexagonal base. Each side of the base is 10 m. Its height is 60 m.The volume of the pyramid is

5196 $m^3$
5200 $m^3$
5210 $m^3$
51220$m^3$

Question 12 Multiple Choice (Single Answer)

A right pyramid on a regular hexagonal base is of height $60$ m. Each side of the base is $10$ m. The volume of the pyramid is

$\displaystyle 4500\ \text{m}^{3}$
$\displaystyle 5000\ \text{m}^{3}$
$\displaystyle 5196\ \text{m}^{3}$
$\displaystyle 6196\ \text{m}^{3}$

Question 13 Multiple Choice (Single Answer)

A regular square pyramid is $3$ m height and the perimeter of its base is $16$ m. Find the volume of the pyramid.

1212 $cu. m$
1414 $cu. m$
1616 $cu. m$
1818 $cu. m$

Question 14 Multiple Choice (Single Answer)

The altitude of the frustum of a regular rectangular pyramid is $5\ m$ the volume is $140\ cu.\ m.$ and the upper base is $3\ m$ by $4\ m$. What are the dimensions of the lower base in $m$?

$9\times10$
$6\times8$
$4.5\times6$
$7.5\times10$

Question 15 Multiple Choice (Single Answer)

The length of the base of a square pyramid is $2\ cm$ and the height is $6\ cm$. Calculate the volume.

$8\ cm^3$
$6\ cm^3$
$4\ cm^3$
$2\ cm^3$

Question 16 Multiple Choice (Single Answer)

The base of a right pyramid is an equilateral triangle of perimeter 8 cm and the height of the pyramid is $30\sqrt 3$ cm. The volume of the pyramid is

$160 cm^3$
$1600 cm^3$
$\dfrac {160}{3} cm^3$
$\dfrac {5}{4} cm^3$

Question 17 Multiple Choice (Single Answer)

A right pyramid is on a regular hexagonal base. Each side of the base is $10$ m. Its height is $60$ m. The volume of the pyramid is

$5196 m^3$
$5200 m^3$
$5210 m^3$
$5220 m^3$

Question 18 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 c.c.
240 c.c.
640 c.c.
900 c.c.

Question 19 Multiple Choice (Single Answer)

If the volume of a prism is $1920$ $\sqrt{3} cm^3$ and the side of the equilateral base is $16$ $cm$, then the height (in cm) of the prism is?

$19$
$20$
$30$
$40$

Question 20 Multiple Choice (Single Answer)

The corner of a cube_has been cut by the plane passing through mid-point of the three edges meeting at that corner. If the edge of the cube is of 2 cm length, then the volume of the pyramid thus cut off is

$\dfrac{1}{24}cm^3$
$\dfrac{1}{6}cm^3$
$\dfrac{1}{48}cm^3$
$6cm^3$

Question 21 Multiple Choice (Single Answer)

Each side of the base of a square pyramid is reduced by $20%$. By what percent must the height be increased so that the volume of the new pyramid is the same as the volume of the original pyramid?

20
40
46.875
56.25
71.875

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