Volume and surface of solids

2010016504

Level: 
B
How much paper do we need to label the can of peaches with diameter of \( 12\,\mathrm{cm} \) and height of \( 18\,\mathrm{cm} \)? (Label covers the side of the can completely, the bottom and the top base are not labelled.) Round your result to \( 1 \) decimal place.
\( 678.6\,\mathrm{cm}^2 \)
\( 1357.1\,\mathrm{cm}^2 \)
\( 339.3\,\mathrm{cm}^2 \)
\( 904.8\,\mathrm{cm}^2 \)

2010016506

Level: 
B
The volume of a right circular cone is \(96\pi\,\mathrm{cm}^3\) and its diameter and the perpendicular height are in the ratio \(3:2\). Find the surface \(S\) of the cone.
\( S=96\pi\,\mathrm{cm}^2 \)
\( S=60\pi\,\mathrm{cm}^2 \)
\( S=96\,\mathrm{cm}^2 \)
\( S=60\,\mathrm{cm}^2 \)

1003191301

Level: 
C
A frustum of a pyramid has rectangular ends and the sides of the base are \( 8\,\mathrm{cm} \) and \( 6\,\mathrm{cm} \) long. Find the volume of the frustum knowing that the area of the top end is \( 12\,\mathrm{cm}^2 \) and the height of the frustum is \( 5\,\mathrm{cm} \).
\( 140\,\mathrm{cm}^3 \)
\( 100\,\mathrm{cm}^3 \)
\( 420\,\mathrm{cm}^3 \)
\( 1060\,\mathrm{cm}^3 \)

1103191302

Level: 
C
A frustum of a pyramid has square ends and the squares have sides \( 8\,\mathrm{cm} \) and \( 6\,\mathrm{cm} \) long, respectively. Calculate the volume of the frustum if the perpendicular distance between its ends is \( 12\,\mathrm{cm} \).
\( 592\,\mathrm{cm}^3 \)
\( 9616\,\mathrm{cm}^3 \)
\( 1776\,\mathrm{cm}^3 \)
\( 248\,\mathrm{cm}^3 \)

1103191303

Level: 
C
A frustum of a pyramid has square ends and the squares have sides \( 18\,\mathrm{cm} \) and \( 6\,\mathrm{cm} \) long, respectively. Calculate the surface area of the frustum if the perpendicular distance between its ends is \( 8\,\mathrm{cm} \).
\( 840\,\mathrm{cm}^2 \)
\( 360\,\mathrm{cm}^2 \)
\( 480\,\mathrm{cm}^2 \)
\( 804\,\mathrm{cm}^2 \)

1103191304

Level: 
C
A builders bucket is in the shape of a frustum of a right circular cone as shown in the picture. Find the volume of the bucket with the top and bottom diameter of \( 10\,\mathrm{cm} \) and \( 15\,\mathrm{cm} \) and with the height of \( 18\,\mathrm{cm} \).
\( 712.5\pi\,\mathrm{cm}^3 \)
\( 350\pi\,\mathrm{cm}^3 \)
\( 2023.5\pi\,\mathrm{cm}^3 \)
\( 2850\pi\,\mathrm{cm}^3 \)

1103191305

Level: 
C
What is the area of a metal plate needed to produce one bucket? The bucket is in the shape of a frustum of a cone as shown in the picture. The top and bottom diameters are \( 23\,\mathrm{cm} \) and \( 18\,\mathrm{cm} \) and the slant height is \( 17\,\mathrm{cm} \). Round your result to \( 1 \) decimal place.
\( 1349.3\,\mathrm{cm}^2 \)
\( 3207.6\,\mathrm{cm}^2 \)
\( 2189.7\,\mathrm{cm}^2 \)
\( 1623.2\,\mathrm{cm}^2 \)

1103191306

Level: 
C
Find the volume (in liters) of a bucket. The bucket is in the shape of frustum of a cone (see the picture) with the top and bottom diameter of \( 23\,\mathrm{cm} \) and \( 18\,\mathrm{cm} \) and the slant height of \( 17\,\mathrm{cm} \). Round your answer to \( 2 \) decimal places.
\( 5.58\,\mathrm{l} \)
\( 5.65\,\mathrm{l} \)
\( 22.32\,\mathrm{l} \)
\( 22.56\,\mathrm{l} \)