If `V` be the volume of a tetrahedron and `V '` be the volume of another tetrahedran formed by the centroids of faces of the previous tetrahedron and `V=K V^(prime),t h e nK` is equal to a. `9` b. `12` c. `27` d. `81`

Prove that the volume of the tetrahedron and that formed by the centroids of the faces are in the ratio of 27:1.

The volume of a tetrahedron formed by the coterminous edges vec a , vec b ,a n d vec c is 3. Then the volume of the parallelepiped formed by the coterminous edges vec a+ vec b , vec b+ vec ca n d vec c+ vec a is 6 b. 18 c. 36 d. 9

If V_(0) is the volume of a given mass of gas at 278 K at a constant pressure then according to Charle's law, the volume at 10^(@)C will be

For a reversible process at T = 300K, the volume is increased from V_(i)=1L to V_(f)=10L . Calculate Delta H if the process is isothermal -

If V is the volume of a cuboid of dimensions a , b , ca n dS is its surface area, then prove that S/V = 2(1/a+1/b+1/c)

Let G_1, G_2a n dG_3 be the centroids of the triangular faces O B C ,O C Aa n dO A B , respectively, of a tetrahedron O A B Cdot If V_1 denotes the volumes of the tetrahedron O A B Ca n dV_2 that of the parallelepiped with O G_1,O G_2a n dO G_3 as three concurrent edges, then prove that 4V_1=9V_2dot

If each edge of a cube, of volume V , is doubled, then the volume of the new cube is (a) 2 V (b) 4 V (c) 6 V (d) 8 V

If the height and radius of a cone of volume V are doubled, then the volume of the cone, is (a) 3 V (b) 4 V (c) 6 V (d) 8 V

Let G_(1),G_(2) and G_(3) be the centroids of the trianglular faces OBC,OCA and OAB, respectively, of a tetrahedron OABC. If V_(1) denotes the volume of the tetrahedron OABC and V_(2) that of the parallelepiped with OG_(1),OG_(2) and OG_(3) as three concurrent edges, then prove that 4V_(1)=9V_(2) .

A cylinder has volume V, height h, and base diameter d. Which of the following represents d in terms of V and h?