# Test: 3D Shapes - Ambitious

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Question 1:   Radius of a sphere placed in a square equals  $8cm$ ,  find a volume of a square.
$512c{m}^{3}$
$2000c{m}^{3}$
$4000c{m}^{3}$
$4096c{m}^{3}$
Question 2:   Find the volume of a tetrahedron with the side of the basis equal to  $2\sqrt{2}cm$ .
$\frac{4}{3}c{m}^{3}$
$1c{m}^{3}$
$\frac{8}{3}c{m}^{3}$
$2c{m}^{3}$
Question 3:   Calculate a volume of the pyramid, with a rhombus in the basis with diagonals  $4cm$  and  $6cm$ ,  and a height of a pyramid  $10cm$ .
$25c{m}^{3}$
$30c{m}^{3}$
$35c{m}^{3}$
$40c{m}^{3}$
Question 4:   A side of the basis of the triangular pyramid equals  $a=4cm$ ,  apothem  $b=5cm$ .  Find an area of the side of the pyramid.
$10c{m}^{2}$
$30c{m}^{2}$
$20c{m}^{2}$
$45c{m}^{2}$
Question 5:   Calculate a volume of a cylinder, if its height is  $h=4cm$ ,  and an area of the basement  $S=10c{m}^{2}$ .
$30c{m}^{3}$
$40c{m}^{3}$
$50c{m}^{3}$
$60c{m}^{3}$
Question 6:   Calculate a volume of a pyramid with the square in the basement and  $h=6cm$ ,  $b=3cm$ .

$50c{m}^{3}$
$72c{m}^{3}$
$64c{m}^{3}$
$82c{m}^{3}$
Question 7:   Find the volume of the sphere places in the square with the side  $a=8cm$  .
$\frac{256}{3}c{m}^{3}$
$\frac{256}{3}\pi c{m}^{3}$
$\frac{226}{3}\pi c{m}^{3}$
$\frac{206}{3}\pi c{m}^{3}$
Question 8:   Projection of the segment  $AB$  on the X axis:  ${A}_{x}{B}_{x}=1$ ,  on the Y axis:  ${A}_{y}{B}_{y}=3$ ,  on Z axis:  ${A}_{z}{B}_{z}=4$ ,  find a segment  $AB$ .
$32$
$\sqrt{21}$
$\sqrt{30}$
$\sqrt{26}$
Question 9:   Projection of a segment  $AB$  on X axis:  ${A}_{x}{B}_{x}=2$ ,  on Y axis:  ${A}_{y}{B}_{y}=1$ ,  on Z axis:  ${A}_{z}{B}_{z}=5$ ,  find a segment  $AB$ .
$\sqrt{30}$
$\sqrt{80}$
$\sqrt{34}$
$40$
Question 10:   Calculate volume of a pyramid with a square in the basement and  $h=4cm$ ,  $l=5cm$ .

$50c{m}^{3}$
$144c{m}^{3}$
$30c{m}^{3}$
$48c{m}^{3}$